The String class uses memory. Plenty. I think you have found the problem - even without looking at the code. When you get close to running out of memory the crashes will be "random" as the stack and the "heap" start overwriting each other, and that means the amount of overwriting is very sensitve to excatly what variables are used and what calls are being made and when an interrupts (which also uses stack) occurs.
Search for and include one of the "report free memory" routines ( fex. memoryFree ) to confirm your diagnosis.
Solving the problem? Use less strings, or put them into the EEPROM memory. Maybe a fixed array where you insert/overwrite some positions with the values to avoid using the String class for string concatonation.