So its been about 6 months since I've bought my fit, and this morning the low pressure light comes on. Turns out my passenger side rear is low.

I put the air in the tire thinking that would do the trick, which it did, but a few hours later, same problem all over again.

Went to the tire store and they state I have a leak close to the sidewall (no nail / screw).. just a small leak.

They are asking me for $145 for a replacement.
Can this be covered under warranty? I'm at 12k miles... and there is sooo much tread on this tire left.

 

At the risk of sounding like a smart**s, maybe you should be asking Bridgestone, if there is no sign of an actual puncture.

 

Same thing happened to me over the winter, only I picked up a nail in the sidewall, so there was no patching it. The local tire shop plugged it temporarily and had to order a new tire. It cost me $170 to replace ONE tire on this car! Some "economy" car, eh?

In your case, check the tire warranty that came with the car or contact Bridgestone directly.