We have something called an "inspection period" where the Buyers have the right to conduct any number of due diligence actions (conduct the necessary inspections, collect paperwork, feasibility, collect bids) to make sure the property is sufficient in quality, condition and use of the Buyer's intended use. 

The importance of income from your deals, being SUFFICIENT, cannot be over-stressed! 

Like a card player going into a game without sufficient reserves for a bad or misplayed hand, you need to bring money into this game or risk losing your shirt.

For landlords, the housing costs are lower while the rents are still sufficiently high enough that you cash flow regardless.Wherever you live though, I guarantee you someone is making money in real estate right there.

If they are taking action, is it sufficient to have the property perform per the budget?

This is known as the self-sufficiency rule.  

If it will then that should not be sufficient for the lender when I refinance the property.

Also make sure you have sufficient reserves to carry it if you have a lot of vacancy and or repairs.

Once you have these reserves and a sufficient downpayment you can pick up your next property and repeat the cycle.  

As Matthew Brill mentioned, there is a self-sufficiency rule for 3- and 4-unit properties funded with an FHA loan.  85% of the market rents on all four units need to cover your monthly payment (principal, interest, taxes, insurance, and mortgage insurance).