It goes from 0.5V to over 1V within abnout 1-2min.

In what situation is that? With or without the remote connected? Both?
Sounds like you have something leaking power somewhere in the amp - maybe a failing cap - but the symptoms are weird...

Workaround: hmmm... I'd try running both the BAT+ and remote terminal off a relay controlled by the real remote wire (gives positive control of the remote terminal as well) if you can find a relay that can handle the current. You might get thumps - haven't ever wired an amp that way... and different amps act differently when it comes to thumping anyway.

Any warranty left on the amp?

/Michael