This is an ongoing issue, unfortunately tech support cannot replicate it so they can't fix it.
Things you can try:
A network reset. I know this sound odd but it's helped me when I've had trouble with neighbor visits.
Close the game. Pull up the app manager and swipe the game away. Turn off your device. Turn off all networking hardware - modem, routers, network switches, etc. Wait 15 seconds. Turn on modem and wait for bootup. Turn on routers, switches, etc. Turn on device. Start game.
For iOS users: someone in the official forum reported that connecting their device to a computer with iTunes and syncing with iTunes solved their neighbor crashing problem.
Try a clean re-install. Swipe the game away, go to Settings -> Applications (this will vary by device) and clear data, then uninstall. Turn off your device and wait 15 seconds. Turn on your device and install.
Does it crash when you go to your neighbor's Krustylands? Somebody else reported they could do that and bypass the crashing. It doesn't solve the problem and it takes a lot longer since you have to go back to the neighborhood to get to the next Krustyland but it's better than not being able to visit at all. If you break your visits up (assuming you have 100 neighbors) you could just do 33 a day like I do when we're hunting invaders (it takes SO LONG to hunt invaders on top of our slow internet that I just can't do all 100).
Delete some neighbors. Try 2 or 3, then restart your device. Keep going until it's fixed or you've deleted all of them. Yeah I know - pain in the ***, but better than doing nothing. Oh, you do have them written down so you can invite them back, right?