Vitaliy,
It sounds like your executable image may have some problems executing. Can you use the debugger to step through your code? There are a couple of possibilities:
1. Your code is getting some sort of Hard Fault that prevents it from continuing to execute once it is booted.
2. Your code does not implement anything that writes to the mailboxes - (either via the ISF Command Interpreter APIs or by direct mailbox writes)
Your Logic Analyzer decode doesn't look quite right to me, but since we know that you are able to send 0 0 in ROM mode and get device info back and that you can send 29 00 FF FF FF FF and have it stop responding (which to me says you are indeed booting to FLASH, but there's something wrong with your flash executable)
I'll try to put my LA on it and observe the BOOT TO FLASH command adn see what mine decodes. I probably won't get to that until Thursday however.
Bottom line - I suggest using CodeWarrior to step through your code (Using the P&E multilink debug probe) and see what is happening in your program.
-Jim McGlasson