Something is causing a disconnect to the database. You should check the alert log for errors or potential traces. It probably depends on how you start the export as well, ie. are you doing local export or remote (loop back) export.
I am not sure if you are aware of this utility. If you type oerr and error code from OS, it will give you the definition of the error.
See below, this is error code from 8i/9i definition but can not see it chaging in 10i. It sounds like you have a problem with OS and Oracle. I would review your Oracle install log to ensure there was no problems during installation. Ensure 10i is compatible with your OS.
oerr ORA 7445
07445, 00000, "exception encountered: core dump [%s] [%s] [%s] [%s] [%s] [%s]"
// *Cause: An OS exception occurred which should result in the creation of a
// core file. This is an internal error.
// *Action: Contact your customer support representative.
An ora-7445 is an Oracle internal error. Basically a condition has occurred which Oracle could not deal with. Because bouncing the database rectifies the problem I would hazard a guess that this is some kind of memory corruption. The only way to find the root cause will be to analyze the trace file that is generated by the error. Unless you know are experienced with these errors you will have to engage Oracle Support and upload the trace file, export and alert logs. If you don't have a support contract the only thing I can advise you to do is to download and apply the latest patchset which I believe is 10.1.0.3. If the problem persists then and you don't have a support contract, your in a pickle. Paste in the entire error. i.e.