Bio-signal discontinuity after FIR filtering
You need to maintain the filter state. For an FIR filter that's fairly easy since the state are just the last $N-1$ samples if your previous input, where $N$ is the FIR filter length.
Most filter functions have a built in option for doing this. If you don't have it just do the following:

Prepend you current frame with the $N-1$ last samples of the previous frame
Run the filter
Throw away the first $N-1$ samples of the output.