As a certificate holder, you will be notified should the policy terminate or lapse for any reason. 

Since I let my license lapse, I have to go through the formal education all over again.

I found that one contractor I hired gave me a certificate of insurance that had lapsed.

One thing I worry about is appreciation in a rougher area but the cash flow seems to work.Potential Purchase Price - $350,000Down Payment - 20% or $70,000Property Taxes - $5,100Gross Rental Income - $50,000 per year (all four units are TAW currently occupied which originally had leases but owner let them lapse so new owner could do as they wish - all rents are current and in good standing)After property management fee's, factoring in some maintenance costs, plowing, lawn mowing, and landlord paid utilities it looks like I will net between $15,000 and $18,000 per year positive cash flow. 

If he is the one who is licensed, and he has insurance to prove it, no need to panic, maybe it is just a lapse, and so i was guilty for that also, while i was doing a fence job for a city client (city yard fencing) you bet they allowed me to continue the work for the next 5 working days, they shouldn't, but they did, under the clause they won't cut the check or tender billing until i get the papers corrected. got proof that the license got renewed (application and payment to renew license), they accepted it.

Are they all currently paid up with no lapses, or does it seem like you'll need to evict any tenants within a few months of taking ownership? 

I'll move everything to the garage and wait until the time period lapses. 

Fayetteville rental veterans: do you tend to have much lapse between tenants?

At that point, how they clear the unit is up to them.An alternative would be getting copies of the lease and seeing if the tenants of your preferred unit have let their lease lapse and are now on month-to-month.

My experience is that renters rarely get it, and those that do get it often let it lapse, and keeping up with it as a requirement of tenancy is a hassle, and you should always maintain your own insurance in case something happens as you damn sure don't want to be relying on a tenant to insure your property.