Can I deduct interest on cash-out refinance (BRRRR Strategy)?

[Keith Thompson]

I'm looking to buy a cash-flowing duplex for cash from a wholesaler and then refinance out later, basically the BRRR strategy.

If I don't use financing for the initial purchase of the house, can I actually deduct the interest on the cash-out refinance on my taxes?  Is there a time limit to get financing on a house before it is no longer considered a "purchase" expense, and therefore interest for the life of the loan is no longer deductable? 

FYI- this is an individual purchase, not LLC.