It still qualifies for First Time Buyers relief as the basis is on the date that the original loan was effected, if the loan was redeemed and replaced by another loan, the revenue ask for the date of redemption and compare this with what is on their record. However often I have seen this making the second loan non first time buyer but generally corrected after contacting the Revenue. Tax Relief is covered under Section 244 of the TCA and makes no reference to lender, only refers to interest, etc. It also states that the qualifying loan are ones used to pay off another loan used for such purpose (purchase, repair, development or improvement of qualifying residence)
However, there was one time that remortgaginge deemed the new loan as non qualifying but this was only for investment properties (post Bacon) but no longer is an issue as they reintroduced Mortgage Interest as being tax deductible.