Atomizers can be pretty variable. I've had some that last months others that die in minutes or are simply DOA.
My suggestion is to always have plenty of spares and juice on hand including repair parts for mods. plus it wouldn't be too bad an idea to just have a second device for a back up.
Personally I've got my costs down to around $70 a month. I'll buy juice and atomizers from Best-Ecig every 2 to three months (usually pick up 5 atomizers and 200ml juice) then batteries from a wholesaler every 3-4 months as well.
This hobby can be fairly economical if you can settle on something you like and just maintain. The people who are spending large sums of cash are the ones who are either still looking for that perfect device for them or who just like having new gadgets
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Personally I ended up into the hobby around a grand before I finally found a device I liked, that was over about a 6 month period trying various penstyles and passthrus until the Prodigy V1 came out and I switched to just buying consumables and the occasional spare (switches could be a bit buggy on the V1)
Now to your specific questions. A cartridge doesn't last very long at all if you mean until it needs a refill. that said when refilling them they can last a long long time. I use 801s and I'll end up changing a cartridge about ever 6 months (usually when something happens to damage it (cig getting turned on for an extended time) other than that I'll occasionally pull out the batting and clean it with water trimming off any hardened parts that need it.
I do a combination of cartridge and dripping basically I keep my cart somewhat damp with juice then drip 2-3 drops in to smoke. It seems to help extend my atomizers longevity.
I tend to use an atomizer until it either dies, has severely diminished vapor production or develops a bad taste. As I said this could take anywhere from minutes to months depending on the atomizer and if I screw up (like the other day when I cooked a perfectly good atomizer by forgetting to lock the screw down on my V3.1 and it went off for like a minute while I was working on my truck).
Batteries tend to be a bit more predictable (as long as you are using manual switches) at least for me. I vape 6v (used to be 5v) meaning I use the little CR123As I try to have 3-4 pairs in rotation and they honestly tend to last about 4 months before they start having serious performance degradation.
This will vary a lot based on your use habits. If you are in pacifier mode batteries will last a significantly shorter time than if you are just taking the occasional puff. There are threads on the board from more technically inclined people than I but basically each battery has a certain amount of cycles before failure, But the performance isn't an instant drop off instead they will gradually drop off in performance until you just decide it's time for a new battery.
Now as to general durability beyond the consumables it depends on the device type and manufacturing standards. The typical device with proprietary batteries are generally cheap throwaway devices. They are designed to be disposable and are.
High quality mods on the other hand can be quite different. They will generally be more durable than the typical device ranging from tough to military grade. simple mechanical devices like the Prodigy and really don't have many failure points and I've dropped mine countless times and others have even ran over theirs with cars and they still worked.
I also consider anything with a PCB to be less rugged than simpler designs it's just an additional failure point and one that is susceptible to a wide rage of potential failures. So something like the Provari or Darwin will tend to be less reliable and rugged than a basic mechanical switched screwdriver though they compensate for that with a different more consistent vaping experience.
In a lot of ways the old saw that you get what you pay for is a fairly good guide to how reliable a device will be over the long haul. a 30 dollar kit is by nature meant to be disposable. The seller would go bankrupt on those if they lasted forever. These are commodity devices that are mass produced using the cheapest parts and processes that can provide adequate performance.
The mod market is a bit different, this tends to be the domain of smaller enthusiast entrepreneurs who are trying to develop the types of products they'd prefer to use. Their manufacturing runs tend to be smaller so they gain less advantage through economy of scale for using cheaper parts and components, They are serving a different and more discerning audience who will flame the hell out of them and bad talk their products if they put shoddy stuff out. These guys tend to be more willing to stand behind their work offering solid warranties. This isn't to say that their aren't some shoddy products in the mod market but you will generally tend towards more reliable devices from it.
Hope that helps clarify things a bit for you.