An outgoing VPN connection from your computer should not be any strange for your router. If you have opened it up, then you better plug all the surplus holes you have opened.
VPN adds a little overhead information to each packet. If you're unlucky, this will make each outgoing packet just a little bit too big, so it will be broken into two packets. This creates unnecessary work for your computer and the router.
I hope someone will step in and tell us where you can adjust the maximum packet size at root.
Otherwise, if too many packets drop out of the outer VPN connection, then it may break. If you happen to use the full capacity of your internet line (say, a couple of bittorrent clients running in unlimited settings), then you better make sure, one wy or another, that you reserve enough capacity for your VPN connection.
If you're using wifi between your computer and router, try connecting via cable and see if this helps.
Radio frequency interference (and or ethernet traffic collissions) could kill enough packets to break your vpn link. This might be a microwave oven, DECT phone or something, but could also be that your network uses not the same, but adjacent channels as your neighbour (1-2 channels away) Metageek inSSIDer will show you what wifi networks are visible from your computer, what channels they're on (and how wide the channels signal is, depending on its signal speed) For 802.11g, it's best to maintain 5 channels difference, the general recommendation is to only use channels 1, 6 and 11 (although lots of home routers totally ignore this).