I just recently leased the 2011 TSX, Non-Tech, and I have the same issues. I have an HTC EVO, and I have to pair them once a month. It pairs fine, but then after a while it won't recognize there is a phone, and when I try to pair from my phone it says "pairing cannot be started from phone," and I have go through the pairing process all over again.

 

I had similar problems with the 2010 non-tech. numerous calls to the handsfreelink help desk, dealer, etc did not solve the issue and I believe it's a "feature" of the complex and somewhat dated design system that is used by Honda/Acura.

I recommend that you do a complete reset of the system (done via verbal commands, check the manual).
you can also hold the "hang up" button for approx 20 seconds and the system will conduct a self-test and tell you if it's ok (in english and japanese, i think!)

Next time you loose connectivity, try issuing the command "next phone", instead of re-pairing the phone. the system will scan for paired phones and link to the next available one. This is what works for me.

 

Whenever I lose pairing, usually the next time I start the car, it'll pair right back. I used to get mad that I had to always re-pair it but now I just leave it alone. Fixes itself from what I've seen. And I can never use the "next phone" cuz whenever I lose the pair, it doesn't have any other phone in the system (even though I've paired under different names before also). It's odd...

 

Had the same issue with my 2010 TSX. I found that it started to happen after I paired my wife phone and then my new one. I thought it was my new phone... brought my new phone back to the store and gave me a replacement, re-paired the replacement and same thing. It would pair but when I shut off the car and turn it back on, it would pair for a few seconds and then just drop off immediately. I then read somewhere that resetting the handfree link database to default, that is to clear all may fix the problem. I tried it and sure enough, it fixed the problem. The instructions on how to clear your Handfree link database is in the manual (quick/startup guide or full user manual that came with the car.