Well, any micro only ever executes 1 instruction at a time, then goes to the next; so it is never really possible to be accessing two ports at precisely the same time!

Usually, accessig a port takes several instructions; eg,
1. read byte from port;
2. store byte to buffer;
3. adjust buffer pointers, flags, etc.

If an interrupt occurs during the process, and a badly-written handler corrupts something which your port access routine was using (eg, the Accumular) - this will obviously cause you grief.
A careless multitasking system could give you similar problems.

Can you narrow this down to a simple example which just accesses the ports - then it might be easier to see what's going on.