WASHINGTON — Mitt Romney’s promise to restore $716 billion that he says President Obama “robbed” from Medicare has some health care experts puzzled, and not just because his running mate, Representative Paul D. Ryan, included the same savings in his House budgets.

The 2010 health care law cut Medicare reimbursements to hospitals and insurers, not benefits for older Americans, by that amount over the coming decade. But repealing the savings, policy analysts say, would hasten the insolvency of Medicare by eight years — to 2016, the final year of the next presidential term, from 2024.

While Republicans have raised legitimate questions about the long-term feasibility of the reimbursement cuts, analysts say, to restore them in the short term would immediately add hundreds of dollars a year to out-of-pocket Medicare expenses for beneficiaries. That would violate Mr. Romney’s vow that neither current beneficiaries nor Americans within 10 years of eligibility would be affected by his proposal to shift Medicare to a voucherlike system in which recipients are given a lump sum to buy coverage from competing insurers.

For those reasons, Henry J. Aaron, an economist and a longtime health policy analyst at the Brookings Institution and the Institute of Medicine, called Mr. Romney’s vow to repeal the savings “both puzzling and bogus at the same time.”