The phrase 'so many times that' is correct and can be used in written English. It is used to refer to how often something has happened. For example: I have practiced my guitar solo so many times that I'm sure I will be able to play it without making any mistakes.
It's so many times that he's lost count.
The doors had been painted so many times that they wouldn't shut properly.
You would get stung so many times that your eyes would swell shut.
He's been bitten so many times that he's immune to the poison.
"They hit the bat so many times that the bat broke," he says.
They had been told they were filthy so many times that they had internalized the sentiment.
(Anton reread the letter so many times that she committed it to memory).
He did this so many times that the walls of his cell were black with soot.
Louima has now described the attack so many times that there are inconsistencies in his account.
"We've gotten our hopes up so many times that at this point, we're pessimistic," Satavy said.
We've turned the other cheek so many times that our heads are spinning".
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK