Many of you know this, but maybe some who've be doing replays don't.
When LSPN comes up and you're ready to play, go to GAME SETTINGS. Under Tour Options, check "Play Offline". You can play your complete round without worrying about losing your internet. If you get to the end of the round and your internet is disconnected, just wait until you know it's restored and try submitting the round again.
I always play offline even with very reliable internet. For one thing, I find it's just better for my routine between shots. Not to have the leaderboard pop-up every hole.
Just a thought.