Stallions are a constant headache - even well-behaved ones. You need a fence that would stop a charging rhino, because heaven forbid that your animal breaks out and makes himself a nuisance to the neighbors. He will most likely need to be confined alone, and will most likely need extra feed because of all the energy he burns off pacing the perimeter of whatever space he is confined to. One of the "rules of thumb" that get passed around among horse people is that, if you buy a mare that may have been at a place that had a stallion on the premises, you should get her pregnancy tested; you might be amazed at how many "whoops!" foals are out there. An awful lot of boarders have been incensed when their mare turns up pregnant unexpectedly; most mare owners won't even consider boarding at a place that houses a stallion (it's unusual, but mares have been bred through fences). Gelding owners will be worried about the stud getting out and beating up their geldings; most would opt not to risk it by keeping their horses at a place that doesn't keep stallions. Very few boarding facilities will take stallions as boarders; those who do usually charge extra.
As kajira said, it takes more than bloodlines to 'sell' a stud - he has to have done something to make people believe he is worth sending a mare to. That means you have to campaign him, or pay someone else to campaign him, to get him the exposure and draw the interest of mare owners. That's time and money, above and beyond the cost of merely maintaining him. If someone sends a mare to you, you have to board her, and if it takes more than one cycle to get her settled, that's more of your time and energy that you may or may not get reimbursed for - there are lots of ways that this can cost more than it pays. A lot of people who keep broodmares send them to the stud while the mare is already in foal or with a foal at her side, which puts responsibility for care of the baby and possibly the delivery on the stud's owner.
The race horse industry arbitrarily assigns January 1st as the birth date of all horses in their registry. Every TB that was born in 2015 officially turned a year old on 1/1/2016, even if it was actually foaled the week before. As you can imagine, this would put any colt born late in the year at a severe disadvantage when it started racing as a "2-year-old." It might not matter as much in performance-based disciplines, but in those where very young animals compete (like conformation classes), age matters, so there is a general tendency toward breeding so that foals get born in the Spring. As a result, even popular stallions tend to stand idle for most of the year.
Locally, "full board" means a stall, two meals a day, daily turnout, with feed/hay/shavings provided, and the labor to get the stall cleaned and the horse in and out and fed. The usual price for that is between $350-$400/month, and about half of that is supplies. Someone built an absolutely top-rate facility with lots of amenities, including hot/cold water in the wash stalls and a covered arena, and tried to charge $600/month - and went broke. It's a tough market.
Most of the folks around here barely break even - they have some other business that brings in the cash, and the horses are a sideline.
