How do I fix a rejected e-filed extension request with estimated payment made electronically?

I can think of only four reasons for rejection. 1) Bad info for the 4868 like your SSN or a bad routing or account number, 2) filing an extension for a return that has already been filed using your SSN 3) filing after 4/15 local time, 4) an IRS issue  

You have until 11:59PM on 4/20 to fix the issue if possible

You can file a tax extension through TurboTax by completing Form 4868 online, estimating your tax liability, and submitting the request electronically.
Step-by-Step Guide
Sign In to TurboTax
Log in to your TurboTax account. 
Navigate to the Extension Section

Select “File an extension” from the left menu.
If not visible, open any section of your return, search for “extend,” and select “Jump to extend.”
Alternatively, go to “Tax Tools” → “Tools” → “File an extension”.

You will need to provide:
a) Personal information (name, address, Social Security number)
b) Estimated tax liability and payments for the year. do not override the balance due calculation. 

Review all information for accuracy.
Submit the extension electronically through TurboTax.
You will receive a confirmation once the IRS accepts your extension. Sources
Keep Your Confirmation

For future years:

1) Consider filing for an extension early once you have a reasonable estimate of your balance due. you can still select the payment date as 4/15 or

2) use the IRS website to file an extension. The same things apply. you can file early but select 4/15 as the payment date. You can print or safe(as a pdf) the confirmation