What made us stop is when we had a Section 8 resident that did some damage in their unit. 

I just had one of my tenants set one of my houses on fire, major damage but not a total loss.

Whereas the neighbor's insurance company or the neighbor may be found responsible for paying future damages caused by their trees.I have a rental house with two neighbors large trees overhanging on both the side fence and also the rear fence encroaching toward my newly re-screened pool cage.

Then I'm left with a damaged property and have to spend so much money on repairs, then look for another tenant who will probably do the same thing.On the other hand I have properties in B grade neighborhoods with an ROI of 14% where I never hear from the tenant and their rent is never a day late.

I had a house with a garage full of termite damage that was found.

The roof and the floors were not huge costs to us the buyer, as the seller filed an insurance claim for water damage just prior to our offer closing.

Also, to clarify an LLC shields the assets within that LLC from inside and outside liability, whereas an umbrella policy only pays damages once you've already been (personally) found liable (if you have the investment property in your personal name). 

I doubt the heat is enough to damage a fan.

The hurricane damaged a lot of homes, so her workload increased.

They actually abandoned the property and caused lot of damages to the property.