It's unlikely that your 1361 transformer is causing the problem. The "Open Circuit" message on the Keypad display almost always means there is a communication failure between the Control Panel and a Keypad, most often a data wire that has come loose or poorly connected, either at the V-20 Panel itself (data wires are terminals 6 & 7), or at one of the Keypads. It could be a loose wire at more than one KP, but that's unusual.
I recommend you go to the Panel (the Vista-20) and find the data wires for each Keypad
(1) Power down the Panel: Transformer unplugged, battery disconnected. Do NOT disconnect or connect KP wires while Panel is powered up. It tends to zap/kill KPs.
(2) Find which wires on Panel Terminals 6 & 7 to which of your 3 Keypads. #s 6 & 7 provide data to/from a variety of peripheral devices, so it may take some searching. The data wires are usually green and yellow/white. See if you can find a loose or loosely connected wire on Terminals 4, 5, 6, or 7. Sometimes those wires are bunched together and you'll need to give a tug on each individual wire. If you're lucky, you'll find a loose one that will fix the problem once it's connected firmly. If that doesn't solve it, then, remembering to power the Panel down first.....
(3) Disconnect the KPs at the Panel (The Vista-20 PCB), one at a time, then power the Panel up again, until you find which KP is causing the problem.After you see which disconnected KP solves the problem, then go to that KP and take it off the wall and check the connections there. The KP itself is usually good, it's most connections that cause the "Open Circuit" problem.
Some KPs have screw terminals, others have wire leads that need to be soldered to make a connection. Some installers use crimp connectors, and I've seen wire nuts used too. If the KP doesn't have screw terminals, I recommend solder-and-tape for a good connection.
Please let me know what you find, or if my instructions aren't clear.