CRJ200 Captain reports stabilizer trim anomalies; resulting in landing at destination airport with flaps 20 and intermittent trim capability.

Narrative

During climb; STAB TRIM and a MACH TRIM CAS messages appeared on MFD (Loss of both Stab Chan 1+2). [We] used QRH to reset stab trim and mach trim systems. After 10 seconds; they both failed again. Tried another reset and they stayed engaged until the autopilot needed to trim for a speed change. We operated the remainder of the flight in this configuration (AP ON and Stab/Mach trim engaged at same IAS). We notified maintenance but they offered no help. The Dispatch Supervisor worked with us on continuing to our destination and the required landing distance with flaps at 20 degrees. We only notified the Flight Attendant of the problem and the higher speed landing. Upon reaching our destination area; we notified Approach that our aircraft would be limited and to have Crash Fire Rescue awaiting our landing in case we lost control during the flare. When the autopilot was turned off for the visual approach the Stab/Mach trim remained engaged; but the manual stab trim was intermittent. With the trim semi operating; the trim for landing was obtainable. Therefore the aircraft was easily controllable at flaps 20 for a landing. Upon arriving at the gate; passengers and dead heading crew deplaned normally without any knowledge that this occurred.