I also have an alarm stuck unarmed. I only noticed today when checking what upgrades were still needed.
Turning it off & on doesn't reset it. Unlike the OP a new alarm does arm for me, it also needs the upgrades added again. My problem with this issue is that you may not notice it's unarmed until the burglar is robbing you :(
This is on Xbox Series X (so no mods or custom content).
Packs installed are:-
Island Living
Outdoor Retreat
Spa Day
Throwback Fit Kit
City Living
Basement Treasures Kit
Desert Luxe Kit
Get to Work
Get Together
Dream Home Decorator
Jungle Adventure
Update: I have since checked previous saves and found that the alarm was armed on 16/3, so this broke on the 17/3 while playing this household. Luckily I didn't play much since the 16th so I reloaded that save and repeated what I did on the 17th and got the same issue. After breaking it down and retesting I have found what broke mine...
Having your power cut off while at another lot causes the alarm to be stuck in a disarmed state.
Doesn't break if your power is cut while on the lot.
Not sure if this is what broke it for the OP or others but it is one issue.
Fixes for the issue I encountered are:-
Buy a new alarm and reapply any upgrades.
-or-
Don't pay the bills and let them cut the power again but while you're on the lot, then pay the bills and the alarm will return to an armed state.