The answer is yes and no.
Yes to the lender’s policy; no to the owner’s policy.
If you obtained title insurance when you purchased your home, that owner’s policy remains in effect for as long as you or your heirs own the home, regardless of any loans you have on the property. The owner’s policy covers your entire investment in the property.
A lender’s policy, however, covers the mortgage. When you refinance—even with the same lender—you’re getting a new loan. And a lot of new issues with the title may have arisen in the time since you purchased it initially. The lending institution has a fiduciary duty to protect the investment. So the lender will require a new lender’s policy.