Once your federal refund is accepted can they reject it?

You submit a tax return; it is a "return of information" to the government about your income and deductions and tax you owe.

If your payments and withholding during the year are more than your tax owed, you claim a refund.

When your tax return is e-filed, "Accepted" only means it passed basic security checks and was downloaded into the IRS system.  It does not guarantee the refund you requested will actually be paid.

The IRS says that about 90% of refunds are paid in 21 days or less.  Some tax returns are delayed for additional analysis and information.  And the IRS has up to 6 years to audit you after any refund is paid.