Historically, a veteran who is eligible for VA benefits, but has not actually received VA benefits in the last three months, can still be eligible to make or receive HSA contributions. Effective January 1, 2016, The Surface Transportation and Veterans Health Care Choice Improvement Act (H.R. 3236) permits veterans enrolled in a HDHP (without any other disqualifying coverage) and who have a service-connected disability to make or receive HSA contributions regardless of when they received VA benefits. The old rule that said if a veteran received any kind of medical benefit in the previous 3 months is no longer effective and does not apply.
Source: IRS Notice 2004-50 Q&A Q-5