Check with your lender about interest-rate reduction refinancing on your existing VA loan. This is a great advantage and there's no need to re-establish VA loan eligibility. Instead, ask your lender to use the VA's "email confirmation procedure". You may also re-use your VA loan eligibility for another VA loan.
The requirement here includes having completed payments on the previous note, and you must no longer own the property. When applying for re-eligibility, include copies of the paperwork that proves your old VA loan has been paid off-a "paid-in-full" letter from your bank, or a copy of the "Closing Disclosure."