Unfortunately, VA usually will only extend a GI Bill delimiting date in three specific situations:
-If you were recalled to active duty, in which case your delimiting date would be reset to your latest separation date. -If you were detained by a foreign power. -If you were somehow prevented from attending school because of a temporary disability - you were in a car accident, had an unexpected job relocation, or were the care provider for a critically ill family member.
In the last two cases, supporting documentation is required, and the last case is extremely difficult to prove.
The Montgomery GI Bill (MGIB) has a 10-year delimitation date (10 years from your date of discharge), and by law VA can't continue paying you past that date, which is different from just running out of entitlement. In the case of running out, VA can pay you until the end of the semester or for up to 12 weeks, whichever is shorter.
Another option would be to switch to the new Post-9/11 GI Bill, if you are eligible for it, as it has a 15-year delimitation date. If you are not eligible for the new GI Bill or don't fall into one of the above categories, then you are most likely out of options.