CRJ-700 Captain reported an autopilot malfunction resulting in rapidly increasing pitch oscillations. The Captain immediately disconnected the autopilot and hand flew the aircraft the rest of the flight. The Captain stated this is a recurring malfunction and the cause is not yet determined.

Narrative

At approximately 7;000 feet while climbing out of ZZZ; I called for autopilot to be engaged. Immediately after activation; the aircraft began a fast pitch oscillation up and down; with magnitude increasing each cycle. I immediately recognized the malfunction and quickly disengaged autopilot. The remainder of flight was hand flown.This is at least the fourth time I have experienced this specific malfunction. The aircraft's pitch oscillation grows in magnitude quickly; and has a logical outcome of reaching a stall; then entering and exiting multiple secondary stalls. Without the certainty of the automation being disconnected; the end result is catastrophic. Depending upon the timing of the malfunction in flight (even if successfully disconnected) it can still remain dangerous.I took the time to explain this to the FO because he had not experienced this malfunction; he previously communicated he was low-time; and my speed in disconnecting the autopilot prevented him and everyone onboard from perceiving the severity of the malfunction if left unchecked.I messaged Dispatch and Maintenance in flight; explaining the malfunction; attempting to impart the importance of switching to another aircraft for the remainder of our scheduled flying; a four leg day planned with Aircraft X. I initially sent the message for Maintenance to Dispatch; and then requested Dispatch to forward that message to Maintenance. Dispatch acknowledged; however I sent another message; this time to Maintenance; to be sure they were notified of the event since we needed another aircraft. It was not as detailed as the first message inadvertently sent to Dispatch; which was to be forwarded.On the ground; I called Dispatch before Maintenance because reply to our in range indicated we were scheduled to keep the plane. After being transferred to the Dispatch Coordinator; and explaining my decision to switch to another plane; the Coordinator said they would work on finding us another aircraft; however he needed Maintenance to place the aircraft in a status that permitted him to make the aircraft change possible. He was agreeable to the solution of changing aircraft after my explanation and was helpful.After a very long wait and additional phone conversations; it was explained to me the Chief Pilot had been called; and per that conversation; the Chief spoke with Maintenance and Dispatch; with Maintenance stating the malfunction is MELable--and per Dispatch we had to fly that plane because we had no other aircraft available. I reiterated I could not accept the aircraft in lieu of the historical context. The Coordinator recommended I call the Chief Pilot and provided a cell phone number to reach him.I called the Chief Pilot and explained my reasons for not accepting the aircraft and provided context of having historical experience with the malfunction. He said he did not realize the malfunction had occurred previously with additional aircraft; nor that I had explained it had happened at least three times previously; four times including this event. Previous flights (best recollection without access to my original reports):The first was also on departure out of ZZZ a few years ago--pre COVID. I was pilot monitoring. After autopilot had been engaged; and pitch oscillations began; I asked the FO what he was doing--he responded 'that's not me.' The oscillation magnitude increased quickly and became large enough for the passengers to realize something was wrong with the aircraft (I learned this later from the flight attendants.). I then quickly said; 'Disconnect! Disconnect!' FO disconnected and I then hand flew the remainder of the flight. I almost returned to the field; however decided to continue as it seemed to be limited to autopilot function. I tested the autopilot again and malfunction reoccurred (stopping immediately with disconnect at the start of the oscillation; which was just as fast however took slightly longer to begin.) Whenarriving in the ZZZ1 area; aircraft; including us; began to receive holds; I elected to notify ATC of our condition: that we are not declaring an emergency; and though I believed we would be fine; I could not guarantee the source of the aircraft malfunction was limited to the deactivated autopilot system or that the autopilot system would remain disconnected--and that we would of course still follow their instruction. I am omitting some details of the exchange and event in this writing. We received vector holding as they gave me the choice between a normal hold and vectoring; and we eventually landed.The next incident occurred at night while climbing; I was pilot flying. The flight and date I do not remember; however it was not in the ZZZ area. After calling for autopilot; I began to review the release. The oscillation was not immediate this time; though it was again a quickly growing climb and descent pattern once it began. I attempted to disconnect; however the disconnect button on the yoke became unmanageable in the dark and associated fast (and accelerating) control movement. I disconnected using the FCP; however the additional few seconds was enough time for the oscillation to become excessive and again make the passengers realize something was wrong with the plane. This oscillation was the worst of all four events.The third time I remember was last year; ZZZ2-ZZZ3. The autopilot was engaged either in the vicinity of 10;000 feet; or above. I disconnected quicker as I recognized the malfunction. The same fast; increasing pitch oscillation was still perceivable prior to disconnect. The fourth time is the reported event associated with this report.Suggestion - I decided to not accept the aircraft because the malfunction has not been corrected; we were flying in an airspace which requires a higher level of safety mindedness and experience; and the issue continues to be a reoccurring event on flights. This strongly implies the source of the malfunction has not been determined; is now accepted as part of our operations; and/or I have not been given relevant information to include among the factors in my decision making. We are not perfect pilots and we cannot have a reoccurring serious malfunction to be accepted as part of normal 121 operations. Consider the malfunction occurring at these moments: Category II approach near 100 feet AGL. Activating autopilot after an engine out on takeoff. Cruise or climb at or above FL280. Recovery from an RA event. Passengers or flight attendants walking in the aisle. Most accidents are a combination of factors. This is frequent enough to reasonably assume this could occur during an emergency event; exacerbating the situation. Simply MELing the autopilot is a reactive action to a reoccurring issue of loss of aircraft control and not a solution; as you do not know when the malfunction is going to occur nor in which aircraft. Please find the cause of the malfunction and establish procedures to mitigate it to within acceptable risk limits for carrying passengers. And please accept it is reasonable for Captains to not accept an aircraft due to this specific malfunction.