Problem with current limiter
Whilst it the sensing circuit should be agnostic as to which upper/opposite lower FET pair of the HBridge is active there is a chance of two possible things going on. Before getting into that though let's first review where the load of an HBridge is connected:



For proper operation of the HBridge it is normally required that either pair of FETs (upper left and lower right) or (upper right and lower left) be on whilst the other pair be off. Electronic breaking of a motor load can be implemented by turning on just the lower two FETs but let us not get into that here.

Problems can come up with your current sensing circuit under one of the possible two scenarios. 


The impedance of your load on the HBridge changes a lot when the polarity of the current through the load changes direction.
The switching control of the four FETs in the HBridge is not being done correctly and one side of the bridge has both the upper and lower FET on (or partially on) at the same time allowing an excess of extra current to flow past the load and into the sensing resistors.  


So you will want to study and make measurements of your circuit to make sure that one or the other of the above situations is not happening.