If you cannot successfully complete an export from the admin system on an own server then it may either be because it has run out of memory or it may have not enough time to execute the entire export.
Try increasing the max_execution_time in php.ini. The default may be 30 seconds, change it to 180 (3 minutes) and see if it makes any difference. If you get more records exported but not all, then increase the max_execution_time even more, to something like 360 and so on until you may get all the records exported.
If you have a lot of overall records then increase the PHP memory limit to 256-510MB.