2003 Camry Transponder Bypass

I hade a profession installed a Compustar 2WFM-AS alarm remote start combo with a 556U transponder bypass, in my 2003 Camry. Everything seamed to work at the shop, but the next morning the remote start only cranked the engine, but wouldn't start. The problem only seams to happen in the morning. If I put a key in the ignition then the remote start works, so I believe it is the transponder bypass. Could it simply be that the receiver loop is just very sensitive and the transmitting loop needs to be in more intimate proximity? Has anyone else seen this problem? Should I suggest that they cut off the plastic sheathing and just get the factor loop and bypass loop closer together. Or am I completely off and it’s something else entirely? I had them add a relay on the cold start ignition wire in the hopes that that was the problem, but no dice. HELP!!

Thanks for the conformation of my suspicion; I’ll tell the installer.

This morning I sat in the car activated the remote start and held a key transponder up to the ignition in different positions and still it just cranked. Then I put the key in the ignition and it started then I removed the key and it still ran. Any chance the key sense wire is incorrectly polarized, needs a diode, or is not connected? The strange thing is it seams consistently time dependent. Is there anything in the Toyota security system that has some kind of time out?