I'm currently using a RF T600-4 to run my RF T1652-S door and rear deck speakers.

I've started to notice when turning on my radio after the car has set for a while the front left speaker doesn't turn on until I turn the volume up a bit. Once it kicks on I can run forever at low or high volumes without it cutting out. Just wondering if anyone knows the internals in a amp that could cause this.

This sounds like speaker wire that is touching metal somewhere. Possibly cut the coat somewhere that the wire is run from your amp to the speaker. Try re-running that speaker wire and see what that does. I had this problem once..