Tax Year Prior to 2020: Is there a limit to the number of years you can file an Injured Spouse form (8379) - due to an outstanding student loan?

There is no limit to the number of year.  The instructions for the form specifically state "You must file Form 8379 for each year you meet this condition and want your portion of any offset refunded."

Form 8379 Injured Spouse Allocation form is entered in this area:

• Federal Taxes tab (Personal Tab in the Home & Business version of TurboTax)
• Other Tax Situations
• scroll down to Other Tax Forms
• then, Miscellaneous Tax form (select Start or Update)
• then, Report an Injured or Innocent spouse claim (select Start)

Here is an IRS article "Seven Facts About Injured Spouse Relief" that my interest you  

IRS Injured Spouse Relief

Also, see these IRS Form 8379 Injured Spouse and Instructions Form 8379 Allocation .