I have an Alpine (CDA-7995) and have never experienced a memory reset (typed with fingers crossed) other than when the battery was deliberately disconnected.
Are you using the OEM wiring for the stereo? How - with svxdc's harness, twisted & taped, soldered, etc? IF you have a newer unit and are using the internal amp, did you run a separate power lead (8 gauge?) as suggested - the internal Alpine amps do seem to have more output (and hence power draw) than the competition.
My best guess without any first hand knowledge is that there is a marginal connection to the constant power line. The A/C draw would lower the voltage a bit, maybe enough so that with a poor connection the system drops it's memory.
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