I wish it didn't rain. / I wish it wouldn't rain.

  1. It’s raining again and we can’t go on a picnic. What a pity! I wish it didn’t rain [color=blue]so often here.
  2. It’s raining again and we can’t go on a picnic. What a pity! I wish it wouldn’t rain [color=blue]so often here.

Source: school exam

Hello,
I know that the above two sentences are correct but what happens if I omit “so often” at the end of the sentences? Are they both still acceptable?

Thank you.

Not really.
“I wish it didn’t/wouldn’t rain here.”
would not be logical. Your wish would be for no rain to ever fall in that place - which would lead to drought.