I'm no expert by any means, but my guess is that you are lacking in watershed and my be looking at a water table pond. You should have about 10 times the pond's acreage for a watershed and your neighbor's pond is using what watershed you have. It is possible that the water table on your neighbors pond is higher than the water table under yours. Water tables are not flat, but will rise and fall with the contour of the land, sometimes against our better judgment in that they do not actually follow the visible contour of the land.

Are you behind on annual rainfall as well?

I can not suggest a fix for this, it is beyond my experience and learning unless a liner and a well is called for, but let's not jump the gun, it seems like the ponds have live with water in them for many years up until now...what has changed?

Any CAFO's get established near you that might be tapping into the water table an making it drop?

Any dirt work take place in your watershed that might have diverted water?

My 2 cents.

Fish on!,
Noel