So you purchased title insurance when you bought your home. Why should you buy more when you are refinancing your own place? While you do not need to buy new owner's title insurance, your new lender will want a title insurance policy, however.
As far as owner's title insurance goes, you purchased it when you bought the home and it remains in effect for as long as you own the property. That means that whether you refinance once or a dozen times, as long as you remain the owner of the property, your title insurance protects you against title defects and hidden encumbrances and claims.
However, the lender's title insurance policy doesn't insure the new mortgage created when you refinance. That means that the lender is not protected. In any case, the prior policy would not protect the lender against things that happened during your ownership period. For example, it wouldn't protect against a second mortgage on the home that might push back the priority of the new lender's mortgage. Likewise, it wouldn't protect again any court judgments or tax liens filed against you.
In addition, many lenders package mortgages as securities. They sell these in the secondary mortgage markets. These new investors won't buy without security to be sure the mortgages behind the securities are valid and enforceable.