Your decision credit score
FHA's rule is published. A decision credit score of 580 or above is eligible for FHA's standard terms. A score from 500 to 579 can still be insured, on more limited terms. Below 500, FHA does not insure the loan at all. The decision score is the middle of your three bureau scores, the lower of two, or the only one there is, and with more than one borrower FHA uses the smallest of their decision scores. It is not necessarily the score a free app shows you.
What a lender adds on top
FHA sets the floor and lenders can add rules above it, so one lender's decline is not FHA's.
Income, debts and paperwork
FHA looks at whether the payment fits your income alongside the debts you already carry, and at whether that income is likely to continue. Pay stubs, tax returns, bank statements, and an explanation for anything that looks odd. Self-employed income can qualify; it takes more paper, not a different program.
The house itself
An FHA appraiser looks at the condition of the property as well as its value, and a house that needs work can fail that review. That is what the 203(k) option exists for.
Occupancy
An FHA loan is for a home you live in. It is not a program for a vacation home, an investment property is eligible only in cases HUD lists, and the file says so in writing.