They are DESPERATE to find insurance and are striking out everywhere!!

If you want to get a clue about places to avoid investing look at states where insurance premiums have jumped or where homes are uninsurable. 

These programs offer options for less money down and in some cases DPA - Down payment assistance.As a banker for over 18+ years I am very skeptical when I hear a new name in the business only because its become tougher to lend with all of the new laws and credit/insurance requirements and regulations.  

For example, we need proof of renters insurance and proof they put electricity in their name.So, it seems odd that you are accepted but they keep wanting more information. 

Also, keep in mind if it causes an undue burden on you or is too costly you can deny them. for example, if your insurance company says that dog breed is on the ban list then you need to find out how much it will cost to insure them. if the rates go up because of the dog then you can deny them based on the undue burden. 

Tax accountant, banker, realtors, property manager, insurance agent, etc.  

Quote from @Erick Pena: A "good" rental property is one that covers all expenses (mortgage, taxes, insurance, maintenance, property management fees, and any other costs) and still leave a surplus (commonly referred to as cash flow).Calculate cash flow as: Cash Flow = Rental Income − Operating Expenses − DebtThere's much more to it, but that's the basic idea.

It’s time to look into home owners/rental insurance.

A good property manager can help with tenant screening, enforce lease terms, and handle evictions more efficiently if it comes to that.Require a Larger Security Deposit: Within the bounds of local regulations, a larger deposit can provide a cushion in case of damage or unpaid rent.Consider Rent Guarantee Insurance: Some companies offer insurance products that can cover lost rent in case of tenant default.

You'll want the rents to at least cover the monthly principal, interest, taxes and insurance (and HOA if there is one).