If you're doing 36 spoke 3 cross wheels with the salsa rim (never heard of it before, but if they advertise it as a 29" rim it should be pretty heavy duty) then there must be something wrong with the building technique. 36 spoke 3 cross is pretty darn strong, I don't think a lack of spokes is your problem. My guess is that it the wheels were poorly built.

There's a lot of disagreement about building a wheel, so it's hard to figure out what's the right way to do it when everyone disagrees. Combine this with a steep learning curve, and it's near impossible. I'll try to simplify it as much as possible.

Unless you're ripping out an eyelet (the hole in the rim that the spoke goes into) or breaking a spoke nipple (the thing a spoke screws into on the other side of the eyelet), you're breaking spokes because they're losing tension. Spokes are very resilient to stretching, but very bad at being compressed. Uneven tension (some spokes having a little too much tension, and some spokes having too little tension) takes away a wheels ability to distribute the load, and places an increased load on individual spokes. This increased individual load can cause spokes to lose tension and instead of being stretched between the rim and the hub (in tension) they become squashed between the rim and the hub (compressed) and are forced to deflect (or bend) slightly in order to not snap. After going through this a couple of times, they start to break. The way to overcome this, is by having a uniformly tensioned wheel, the phrase "a chain is only as strong as its weakest link" applies here.

So far most peoples wheel philosophies agree, even tension is the key to a durable wheel. Some people do however disagree about how to achieve and maintain that even tension. Some shops will use loctite between the spokes and nipples. They argue that once even tension is achieved, then you want to lock it in place so you don't lose that setting. I disagree with this, and think that loctite is a terrible idea. The problem is that when you're tightening a spoke (which you do by turning the head of the nipple) you can also be twisting the spoke. When you twist a spoke, the tension increases. You can have a bunch of twisted spokes, glued into their respective nipples, in perfect uniform tension. The problem is that there's nothing to keep the spokes from untwisting besides the friction between the eyelet (on the inside of the rim) and the nipple (again, on the inside of the rim). Once you ride your bike down the road and bounce all around, the spokes become untwisted, and you hear the familiar "twang" sound from your wheel, like a rock hitting your spoke. All of a sudden, you have one spoke grossly under tensioned. Repeat this a couple of times and you start getting broken spokes due to the lack of uniform tension. The solution (according to me, just a random person on the internet) is to not use loctite, but some lubricant that allows the nipple to freely spin along the threads of the spoke, so whatever your personal choice of voodoo magic spoke oil. Like chain lube, there's many options. There's linseed oil, chain oil, anti-seize, Phil's tenacious oil, Phil's spoke oil (is that a thing?), teflon grease, spit, etc. I use anti-seize because I had a problem of nipples breaking in half with the spoke snapping off too. I think any lubricant is probably ok, and the differences are probably marginal.

Beyond choice of spoke prep compound, build technique plays a role. While building a wheel, it will seem that nipples and spokes are set in place but in reality they still haven't figured out where they'd like to settle. It's just like how most shops will tell you to bring your bike back in after 50 miles so they can do a tune-up due to cable stretch, the same goes for wheels. The thing is though, it's not cable stretch (or spoke stretch). It's the ferrels and hosing settling and being compressed to their limit, or the spokes and nipples getting set into the hub and eyelets. Most good builders will try to pre-stress a wheel while building it in order to set the spokes and nipples into place before the customer picks up the wheel and becomes upset that it quickly comes out of true and starts breaking spokes. There's lots of techniques and disagreements about pre-stressing a wheel, but regardless of your preferred method it will happen (either in the shop while getting built, or on the road while getting ridden on). After it happens, you'll more or less have to restart the tensioning process. Getting all the spokes uniformly tensioned again. After this retensioning (assuming the spokes have been properly stressed by riding or shop manipulation), your wheel should be fine for many many many miles. Maybe every 3,000 miles they'll need a little attention, but not much.

Now that I'm looking at what I typed out, I didn't do a good job in simplifying wheels, let me try again.

TL;DR
1) The spokes in a wheel need uniform tension
2) Spokes need to be able to move around freely and figure out who they are
3) Spokes will rebel
4) Spokes need to be rehabilitated and brought back into line with the rest, achieving uniform tension
5) Spokes won't break anymore, you win.