This is good to know, thank you.
I work in a hangar full of Navy retirees/veterans, mostly enlisted. I know of 2 19.5ers as you call them, one a Navy Chief, and the other a Marine Gunnery Sergeant. One got a DUI, the other was caught taking liberties with female recruits while on recruiting duty. In my experience, if you are removed from the armed forces at 19.5, you did it to yourself.
In these leaner years, they are causing more up-or -out discharges/ resigned commissions. When I enlisted in the Navy in 1992, an E-5 could make it to 20 and retire. That was lowered to 12 in the mid 2000’s, and raised to 14 last year, but a large number of E-5’s get forced out at that point. On the Officer side, zones are delineated by an officer’s career field, so there is no hard and fast up-or-out date. The zones for this year are found here: http://www.public.navy.mil/bupers-npc/reference/messages/Documents/NAVADMINS/NAV2016/NAV16273.txt
For all designators, you can assume promotion to O-3 at 4 years. It looks like the Senior URL (Unrestricted Line) Officer in zone had 6 years time in rank at the time of the board, so you are looking at a max of 10 years at O-3. The senior URL LCDR had 5 years time in rank at the time of the board. We don’t know what his time in service was when he made O-4, so I guess the up-or-out time for O-4 is 15 or 16 years, and all O-5’s make it to retirement. Somewhere in that time as on O-4 you had to screen for command, probably at the 11-13 year mark. at that point you will know pretty much whether or not you will be promoted to O-5 as a URL officer.
Of course, this all Navy, and you asked for Army. Someone might find these numbers for Army.
I knew a lot of Navy guys who retired at 19.5, but that was because the Navy had something called “constructive time”. You could accrue up to six months constructive time by reenlisting early or through other means. What that meant was you could retire at 20 years, less whatever constructive time you had acquired. I joined under something called the “Cache Program”, wherein my enlistment was delayed by four months, so I could have retired at 19y8mo.
Don’t forget the infamous “I’m getting out at 19.5, just so my ex-wife doesn’t get half my retirement!”
I remember it well. As it turns out, that’s not the case unless a judge says so.
Kind of hard to give half of zero.
Edited to add: Actually, I guess it’s easy 
OTOH, if you’re found to have done it deliberately, that’s called despoiling the community. You can end up owing half of what you were supposed to have gotten as your GI retirement if only you hadn’t sabotaged it.
Good luck finding a job that will pay well enough to do that and also leave you money for food and shelter.
So I’m still not clear, as someone looking on this from north of the border. The only serious discussion of this topic I’ve seen is in Jack Reacher novels. When you say “causing more discharges”, what do they do to a guy who’s hit 14 years, say, and hasn’t moved up enough or fast enough? Do they just tell him he’s out? Or do they hint he should resign or he’ll be supervising the West Point sewage treatment plant? After all, if a guy’s determined he’ll at least make that 20 years, then he has to be forced to go somehow.
It can be complicated.
For Officers, they generally have an “up or out” rule where if you fail to be selected for promotion to the next rank for two years, you have to leave the military. Once you hit 20, they can entice you to leave before that promotion gate by telling you that you aren’t competitive for promotion, and you won’t be given a job that makes you competitive, therefore you’re wasting your time and you should leave on your own. They can also give you a really crappy job in an area that no one wants to go. If you take it fine, the job is filled. If you get out, fine, that’s what we wanted anyway.
For Enlisted, there is sometimes an effort to reduce manpower, and there will be a selection board to send people home. Generally they use something called “high year tenure” or a variation of that when you have to be at 'X" rank by “Y” years or you get orders to leave the military. They can also do the same drill, as discussed above to entice you to go home.
“Next time I’m just gonna find a woman I hate, and give her half of everything I own.” - Anon. country western singer
After the Civil War, many officers (like Custer, but also his subordinates) had to take a drastic drop in rank if they wanted to stay on in the postwar army. It was a common courtesy to address them by their former rank.