Without being able to see or reproduce the issue, my best guess is that somewhere the forum POSTs to an index.php page, and when it's redirected to strip index.php out of the URL, then the POST data is lost... But that's only a guess.
If you want to exclude your forum section from these rewrite rules, then this condition should suffice.
RewriteCond $1 !^forum(?:$|/)
This would go in front of each of the two rewrite rules. Keep in mind that this might not be the best solution, but without being able to troubleshoot, I can't even be certain of the problem.