Terry Cox made a good point about using only 5200 below the waterline. 4200 is a very similar compound but with but about 60% of 5200 (if memory serves). This deliberate 'weakness' is meant to make parts bonded with 4200 easier to remove, should that become necessary (such as with deck hardware, which I think is Terry's point).
The NUMBER-ONE reason for 5200 adhesion failure is poor preparation of one or both mating surfaces during installation. In reality, the stuff itself does not fail. You did not mention how well you sanded and prepped with solvent. The presence of even a little dust or dirt in a bilge can render the application of 5200, even if otherwise well-done, pointless. Also, there are TWO absolute Achilles heels with 5200/4200/4000UV compounds: gasoline (you cannot repair a fuel tank with it) and denatured alcohol (a good acetone substitute for really anything but prepping for 5200. The 5200 will simply NOT stick to even the least bit of residue of either one.
(I'm not mentioning silicone residue here because I don't care to get worked-up about it now. If what you're replacing was ever installed with any silicone at all, you're SOL on that.)
MY advice would be to dismantle the whole thing, mechanically scrape and clear away all the residue to start again.
Use a good piece of fiberglass, like a flat-ish scrap (cutouts from cockpit speakers are great) or a new piece (such as from mcmaster.com). It doesn't need to be much more than 3/16" thick; but it needs to be large in area. All of the working of a seacock is in wracking it back and forth, from turning the handle. Good bonding with the 5200 and large area for the backing plate will spare the 5200 seam from the stress.
Plywood can be used for a backing plate but only if it's marine-grade and thoroughly saturated in WEST epoxy. As this might be judgment call, I'd advise going with a piece of fiberglass, or Coosa. Metal, StarBoard, and other plastics, or waferboard (yes; I've seen all of these done) must be strictly forbidden. Don't over-think it - do what's known to do well.
Sand and shape both the inside of the hull and the backing plate to get a pretty good fit. Gaps are okay if, in general, it fits flush to the hull. Typically I grind the fiberglass right down to bare green 'glass (no gelcoat, no paint). Wash the whole area, inside and out, with acetone - several times. Vacuuming might be good to start. Typically I blow the dust away or wipe it away with a paper towel, and then I use the acetone, flipping or exchanging the rag often, to remove all the rest. Sand and acetone-wipe the seacock base and the head of the through-hull as well - this is one area for failure many people overlook. If it's metal, degrease it well (like with methylene chloride) and THEN wipe down with acetone.
Run the 5200 bead around the outside perimeter of the backing plate, in a bead like 1/4" or more in diameter. Make a bead around the inside hole as well. Put at least as much on the bottom of the seacock. Have the outside guy add a fatter bead to the inside of the through-hull flange (not necessary to do more than a tiny bit on the threads; it will find its way onto them and that'll be enough), and then both of you should assemble the whole arrangement - through-hull, backing plate, seacock body, together. One or the other of you turns his part till the desired attitude of the seacock is achieved inside (ensure the handle will swing fully each way; parallel to the centerline is best). Then the outside guy with a large flat file or a special tool like the ones I make turns the through-hull home while the inside guy holds the seacock in position.
As the ooze comes up, wipe it around the edges of the backing plate, the seacock body, and the through-hull, like for fairing it. When you cannot rock the seacock (when there is no noise or additional ooze if you do), STOP turning. With a finger wipe the rest of the 5200 around the seam, like to fair it finally, and you are done.
Leave it sit for at least a week. Don't paint over the 5200 yet, don't attach or work the handle, DO NOT attempt to attach the hose, DO NOT MESS WITH IT. I've broken them loose (due to impatience) at like a week plus. It can happen, especially when forcing on the hose (especially Type-148 septic hose! - another reason to use Marelon is that their hose tailpieces are made for real-world hose installations, not the dated standards of wire-loom India-rubber hose as used in the 1940s).
I like that Joe included a diagram but I don't like the second diagram at all. What attaches the backing plates to the hull? That diagram shows buried bolt heads to attach the seacock. If one of them spins free , the seacock gets loose and you'll get a leak you can't fix. Don't do it that way. If your seacock has bolt holes, you can either ignore them (for example OEM-style Forespar Marelon seacocks, the only ones I use, have, and need, no bolt holes) or drill them all the way through the backing plate and the hull, at which point you are constrained to use only bronze mounting bolts which will be a point of regular inspection for the life of that seacock.
I respectfully disagree with NJLarry because I know 5200 to be absolutely the strongest thing for underwater fastening in the market. All respectable boatbuilders install lead keels with 5200. My boat is 47 years old and any original 5200 is still holding. The tensile strength is only one of the reasons (LifeSeal is like half the strength; and I stopped using Sikaflex after I found I could not work it even during installation - it turned into silicone-like boogers). The real reason is the chemical compatibility with fiberglass and most resin-based plastics and the sheer durability of the compound once it's been properly installed. For example, Marelon seacocks are corrosion-free and extraordinarily durable. Install one and you're looking at 40 years or more in regular saltwater use. You can't say that about bronze ones. If you were to install, properly, a Marelon seacock with 5200, it's essentially a life-of-the-boat installation.
Raider Yacht and Cherubini Boat have used Marelon seacocks with 5200 exclusively since I've been directly involved with them. I've never seen a single hassle with them.