grammaticality - "The problem is he is stingy"

I have this sentence:

The problem is he is very stingy with his money.

But I feel it sounds weird or even wrong with the two ises so close. Is the sentence structure grammatical? If it isn't, how to fix it?

Answer

It's perfectly grammatically correct.

The problem is just that: you repeat the word "is".

It's that simple.

It's a commonplace in English, say speechwriting or advertising writing (I mean say for radio or TV voiceovers), that you don't repeat a word in a sentence or, really, in a passage, and particularly not close.

Here you have two "is"s very close, so it sounds awkward. It's that simple.

(AND INDEED, he/his are almost the same word - that's another repeat.)

The solution is this simple:

The problem is this: he's very stingy with money.

The problem is: he's very stingy with money.

or any other combo.

{Note - it goes without saying there are many other situations where, for emphasis, for drama, because you are Winston Churchill, etc, you repeat a word closely. Say ... "May the luck be with the player." .. repeating the "the" sounds cool and dramatic there. But in the example at hand, it's simple: the sentence sounds lousy since you have (indeed two different) close repeats.}