All the staff wish (that) you weren't leaving so soon.

The sentence sounds perfectly natural and easy on the on the ear. All the staff is sad or feels sorry about the situation that you are leaving so soon.

All the staff wish (that) you didn't leave so soon.

This sentence doesn't sound good or make much sense. However, if we rephrase this sentence as follows, it may sound OK:

All the staff wish that you didn't have or need to leave so soon. Even then, the first sentence with "weren't" is preferable.

All the staff wish (that) you weren't leaving so soon.

The sentence sounds perfectly natural and easy on the ear. All the staff is sad or feels sorry about the situation that you are leaving so soon.

All the staff wish (that) you didn't leave so soon.

This sentence doesn't sound good or make much sense. However, if we rephrase this sentence as follows, it may sound OK:

All the staff wish that you didn't have or need to leave so soon. Even then, the first sentence with "weren't" is preferable.