It is a yearly determination as to whether it is "maintained;" so no.
A more interesting question might be what happens if the organization ceased to be a non profit. Arguably, it could be resurrected. Should the plan be adopted by the non-eligible employer for such an eventuality. Just speculating.
Without any actual detail of the plan, this seems about right. Since your dad never made an election prior to his death then he would fall under the QPSA rules. Essentially he was a vested terminated participant who was assumed to have made an election the day before his death of a joint and 50% annuity. Then he dies and his surviving spouse is eligible for that 50% benefit as a single lifetime annuity.
NonProfit GC, IRC sec. 408(k)(6)(E) says a governmental or tax-exempt employer cannot "maintain" a SARSEP. The IRS usually interprets "maintain" as applying to plans in the present tense, on a continuing basis, not to simply the time of formation.