How is the fence support compromised?

What about during normal rain ... does the lot drain?

It looks to me that the gap that should be below the fence is nearly non-existent.

It also looks like there's a slab on the other side of the fence, probably pitched to the fence so the water has nowhere to go.

The fence post is leaning into the neighbours yard, durring a heavy rain there isn't a lot if standing water but the ground is really soft and saturated in those areas. I think the slab is just some boards laid on the ground to close off the gap under the fence, are you thinking this was the root cause of the problem?

"I think the slab is just some boards laid on the ground to close off the gap under the fence... Let's find of for sure what it is. There should be a gap under the fence.

Relative to the fence, if a bathtub full of water were suddenly dumped at the base of the fence, where would it run?

Ya they are just some rounded 4x4 posts the old neighbours put there for there small dogs. If a bath tub of water were dumped by the base of the fence some would run along the fence and some would run away from the fence towards my deck into the low spot.

You need to determine if the low spot near the deck can be filled and the area will drain, or if a path for drainage must be excavated beginning at the "low spot" and clearing the path for water to drain to an even lower spot. With ponding water, you're always looking for a place where the water should go and how it will get there.

It would be good to remove those boards at the bottom of the fence so that there is an air gap.

Thanx for the advice, I will try and raise the grade slightly by the deck and I think I will try and put a French drain in along the fence.

I wish we had consistent definition for "french" drain. To me, it is a "dead end" cavity in the ground where water is quickly put out of sight and then gradually seeps into the ground. It may work for you here if the water volume is low. It is always inferior to proper grading and generally inferior to regular drains (where water runs to a lower grade where it is let out of the pipe).