What is the best approach to an again and again wobbling rear wheel For the last ten years, I have been riding a mountain bike (Specialized/Rockhopper), and often rather wildly, through rough terrain (roots, jumps, ruts). I am around 110 kg (240 pounds).
As a consequence, my back wheel often starts to wobble after some dozen rides, typically coming with the loss of one or more spokes. My cure so far was to bring it in the shop, and get the spokes replaced, and the wheel was true again. There are rarely issues with the front wheel, but it happened too.

However, in the recent two years, I have only ridden on pavement (roads and bike trails), and it still happens a lot now. I have the feeling that the back wheel is just beyond its life, but I'm not sure, and I really don't have the knowledge if this makes even sense.

The question is, what is the best/right thing to do now:


I can keep going to the shop every other month, and get the rear wheel trued-up. Costly in the long term, but works.
I can ask them to replace the rear wheel. A lot more cost, as the cassette needs to be transferred, and this would open a can of worms, the cassette is over ten years old and maybe should be replaced too, and when doing this, the derailleur, the chain, and the front sprockets also should be replaced, so I'm quickly nearing the price of a new bike. It might still be the best option, though.
I can buy spokes and a spoke key - should be cheap - and learn to fix that myself. That is at the moment my favorite idea, but I am not sure it solves the issue.
I can remove all spokes, to see the true form of the rear wheel (which is probably badly bend). Then I bend it back to about straight (or replace it), and add all spokes back in. I don't know if that approach makes any sense; it sounds like a lot of effort.
I can toss it and buy a new bike


I am looking for someone experienced with such repairs, who is not interested to make the most money off me, to tell me what is the best approach. What makes sense?
Unless the cost of a new wheel that's suitable for you plus any other repairs the bike might need is greater than what the bike is worth to you, than the answer by far is get a new wheel. 

Folks in your weight range who ride a lot tend to need an especially strong and reliable aftermarket wheel. The stock advice is to get a handbuilt one. The reason for this is that a good handbuilt wheel has a number of processes done to it that make spoke breakage and loosening much less of a factor, to the point of never occurring if everything goes right. But that sort of wheel is usually around twice the price of a replacement wheel that at least has the fundamentals covered for what you need (strong rim). A conscientious mechanic installing that sort of wheel on your bike will see that you would be best served by handbuilt and be able to do some of those steps on a cheaper machine-built wheel without adding a bunch of time. (The big example being making sure the spoke tensions are high and balanced, and stress-relieving them).

The cost of handbuilt wheels can be considerable, but another way of looking at them is they're not really optional if you ride enough and are heavy. Otherwise one is liable to spend several times their cost getting the stock one fixed, as you've experienced.

Swapping the cassette on to a new wheel in and of itself and adjusting the rear derailleur if needed is easy and will work as well as it did before, more or less regardless of drivetrain wear. If you need a new drivetrain and feel it may not all be worth it, that's a separate consideration. It is true that new rear wheel time can be the moment where a bike is deemed not worth fixing.