Again, just because Rockbox shuts down in this way, what evidence do you have that that causes the power up problem?
You responded not by showing any evidence but by saying "I know how Rockbox shuts down." So what? What bootloader thinks it's a forced shutdown? Are you suggesting OUR bootloader thinks it's a forced shutdown?
My point is that your statement regarding it shutting down and some "modified bootloader" (we don't modify anything, we add a second bootloader that gets loaded after the main one, which is the one that causes the problem, and also the one that is NEVER MODIFIED, regardless of whether you install Loader2 or the Rockbox loader) is mostly nonsensical. You claim that how Rockbox shuts down causes a problem with another piece of software, and that the fix is to replace a different piece of software that doesn't actually interact in the chain of events you claim is the problem.
So I repeat: What evidence do you have?