B737 Captain reported failure of a hydraulic system resulting in a diversion to a nearby airport.

Narrative

During the non-sterile-climbout phase; we received the #1 Engine Hydraulic LOW PRESSURE annunciator / caution light. We ran the appropriate QRH checklist and noted that System A (and System B for that matter) both had normal quantity and pressure readings; with no fluctuations in either. We contacted Dispatch and Maintenance to discuss the issue. Maintenance and I spoke about the light; went over the Hydraulic System readings together; again verifying that System A still had 92% quantity and approximately 2990 PSI; which had been the same since departing. With no leaks detected; and a stable system now running on the Electric Pump; Maintenance; Dispatch; My First Officer; and I all agreed that we felt comfortable continuing the flight to XXX while monitoring the system. We arrived at our cruise altitude a few minutes after.However; approximately 10 minutes later; the System A Hydraulic Quantity rapidly decreased to approximately 19%; with the system pressure decreasing accordingly. We ran the appropriate QRH checklist for this new issue and [requested priority] with ATC. I made the decision to turn the aircraft around back to XXX; as we were only approximately 30 minutes into the flight; with XXX being the most suitable airport for not only safety and close proximity; but with passenger and maintenance interests in mind. We contacted Dispatch and Maintenance Control once again to inform them of the Loss of Hydraulic System A now; and I informed them of the [priority request]; and that we were returning to XXX. Both parties concurred with this decision as being the safest and best course of action as well. I fully briefed our flight attendants on the [situation]; as well as the passengers. We returned to XXX with an uneventful approach and landing while complying with the remainder of the QRH checklist; and taxied to the gate. Maintenance met the aircraft; and I entered the appropriate maintenance entries into the logbook. I then contacted the Chief Pilot for the debrief.