Troubleshooting Oracle ORA-08103 - object no longer exists
How intermittently are you getting the error?

Do you have any logging in the trigger that is truncating a partition? You could use a simple procedure that writes (in an autonomous transaction) some information about which partition is being truncated.

Also create the on servererror trigger as suggested by Leigh Riffel, and log the query and error stack.

Finally, I would enable tracing of all occurrences of the long running query (assuming this query isn't executed all too often!):

alter session set sql_trace = true;
alter session set tracefile_identifier = wrschneider08103;


before the query and

alter session set sql_trace = false;


after.

Then, once the error has again reared its ugly head, run tkprof on the last trace file with 'wrschneider08103' in its name...

Hopefully you'll be able to correlate the information you've thus collected.