Refinancing doesn't change your cost basis. Only permanent improvements that add value or extend the longevity of the property, such as a roof, furnace, etc. You can also only claim improvements that are still part of the home. If you replaced the roof twice, you can only include the cost of the second replacement. Repairs that keep the property in as-is condition are not improvements. You also have to subtract any casualty losses you claimed and any depreciation you took or could have taken for business use of the home (home office, day care, rental, etc.)
You should keep important papers related to your house for as long as you own the house, plus 6 years after. Make the best guess you can, but beware that if audited, the IRS does not have to award any basis adjustment you can't prove.
