If you have indoor parking, go for it! But just like having a car sitting in another location, you want to be concerned with petty theft of parts , rot, and other things.
some important things to keep in mind:
you wont know who is messing with your car while you are away
it would look like you are throwing away money having it legal while you are gone ( but not really, do the math)
you will need to take out the batteries, and some important fuses/cables to make the car inoperable, while you are gone. keep these in your home, not the car
Dont let no one hold onto the keys
cover your car is a smart thing to do for long periods
know what you are doing if you keep the car on blocks , while you are gone. you can mess up your suspension keeping it hangin for long periods.
I could tell you from experience, leaving the car , even with a trusted person , could turn out bad. We left a car, on blocks, stored in a shed. we had a trusted friend look after it, but made the mistake of leaving the keys.
we returned to find dents on the car, as it was taken out for a spin anyway.
One thing I have learned from my tio, owner of 3 mint Datsuns from the early 70's , is that you cant trust nobody with your babies! He keeps his toys locked up in a shed, and takes the keys with him.
But lets look at the big picture, about $500 a week for a decent car at the rental counter ? How many weeks in the year would you be in need ? You can get a pretty nice used 4x4 to beat around in while you are in the DR. I know many people that do very well with a used Montero,
Prado, CRV, Hilux....so, ballpark, 6 months/ 26 weeks a year in the DR, $10-12 k in rental costs, every year or a 1 time investment + insurance and tags ? If you are planning to stick around like this for a while, go buy yourself a car.