BLUE TONGUE SKINKS

So my BTS, who i've had barely over a month, has mites. These are smaller tannish mites most likely caused by the reptibark i'm using as a substrate. He's been taken to the vet and checked out, and we're currently going thru the process of cleaning out his cage thoroughly every week, throwing everything away, and bathing him as well in a solution that will kill the mites, per the vet's advice. All that said, the skink himself has lost a bit of weight and doesn't really want to eat much. How long can a skink go without eating? I'm sure/hoping that once he feels better and bug free his appetite will pick up. But how much time do I have before having to take more drastic measures?

I've had males to go just about 4 months without food. If the spine and hip bones are protruding out and are defined, then I would look into assist feeding, or whatever your vet feels the right thing to do is. There is not a certain amount of time a BTS can go without food. It would raise some red flags if he is rapidly losing weight and his conditions don't look good overall.

What color are the mites?

Snake mites (reptile mites) are black in colour and you will likely see them on your skink's head in particular. If snake mites you will also see tiny white spots on your skink (particularly back) which is mite waste. Do you have these signs?

I have made a few posts in the past when I've had to deal with mites. Typing 'mites' in the search box above will give you some good hits. Also these are where I have pulled together info while treating mites and you might find these helpful:
Our first shed!!! AND bonus mites
Ugggg in quarantine for mites

If it IS mites, it's not unusual that he is a bit grumpy and off his food. And if it IS mites I would definitely treat them aggressively as I describe in my links above and continue treating for the life cycle.

However, mites are NOT the light brown that you describe so what you are seeing is likely something else. Did the vet identify them? Not sure if this is what you are seeing: Wood lice?.

EDIT: Oh, and it's not unusual to have to treat a new animal for mites (and possibly other things). They bring them home with them. Do you have any other reptiles?

How long your skink can go without food before you need to worry would depend, first of all, on how old it is and/or the size and condition.
If it's a very young skink, it should not go terribly long without eating. Same for a skink in poor condition.

What concerns me about your account is this: if your vet has seen your skink and determined that the tan critters crawling on him likely came from the substrate, then he should've known better than to recommend medicated baths to kill the mites on the skink, as the "mites" that come in wood substrates are absolutely 100% harmless to your skink and do in fact not live on live animals (or reptiles); get rid of all wood and anything that remains after a good cleaning will in fact die off on its own.

Juvenile snake mites are in fact a very light color and can be mistaken for wood lice, but your vet should've been able to determine which they were.

When I just got my bluey she had mites. I took her to the vet and they gave me Frontline(for cats). I put it on a cotton pad(for removing make-up) and wipe it all over her body every week. It worked really well and after a shed the mites never came back. I suggest you to try the same but be very careful because Frontline is relatively strong poison. From my own experience it didn't cause any problem. But I've heard snakes died from using it incorrectly.

And also you have to clean the enclosure thoroughly with frontline as well. Also don't leave water bowl in the tank after you apply frontline on your skink because it is only poisonous as liquid.

If you read up on the lifecycle of a snake mite, you will see they generally lay their eggs away from the reptile. Depending on the conditions where the eggs are, the hatch-time can vary greatly; after hatching, the mites will go through a period of time before they start feeding, but they are masters at migrating from wherever to find a reptile host to live off of.

Frontline is fine to use on BTS, but (from what I've read) a more effective treatment on habitat, and furnishings that can't be baked, boiled, or frozen --whether inside the tank or the ones in the room(s) where the reptile has been, including carpet and rugs-- is Provent-a-Mite, which is safe for reptiles as long as the liquid has been allowed to completely dry.

Whatever you use though, you must either follow your veterinarian's instructions completely, or do careful research on how to use the products for a BTS.