What is a reasonable time for the IRS to cash your check?

Per the IRS website, if it's been at least two weeks since you sent the payment to the IRS and your financial institution verifies that the check hasn't cleared your account, call the IRS at 800-829-1040 to ask if the payment has been credited to your tax account.

You could also get a transcript of your account which would show the payment if it cleared

https://www.irs.gov/individuals/get-transcript 

If you wrote the wrong tax year, the wrong SSN or wrote nothing on your check and did not include the voucher, that can cause problems.

@berndrwolf