I am running into a problem where I update a formula in a cell that is linking to another cell with absolute reference ($) using F4 and the Formula (='tab'!$A$1) is displayed instead of the value.

It is like the Ctrl + ` has been hit but only for that cell and it can't be turned off.

If I re-paste-link it is fixed but that is taking a lot of time.

Any ideas on how to correct this?

See if any of these do the trick:

Press F9 Calculates formulas that have changed since the last calculation, and formulas dependent on them, in all open workbooks. If a workbook is set for automatic calculation, you do not need to press F9 for calculation.

Press SHIFT+F9 Calculates formulas that have changed since the last calculation, and formulas dependent on them, in the active worksheet.

Press CTRL+ALT+F9 Calculates all formulas in all open workbooks, regardless of whether they have changed since last time or not.

Press CTRL+SHIFT+ALT+F9 Rechecks dependent formulas, and then calculates all formulas in all open workbooks, regardless of whether they have changed since last time or not.

And as a last resort, sometimes cells cannot be corrected. In that case, copy the formula so it is handy. Then go to a blank cell and drag it to this position and when it asks to replace, do so. Then copy the formula into that newly positioned cell. Works every time.