As receint as this week I had a classic in with cutting out, (MGB) and traced the fault to poor instalation of an aftermarket Immobilisier/alarm, this was one which broke the ignition feed with a relay when the system was armed, and the state of the install was dire to say the least and I removed it and converted the cars wiring back to standard.
Points worth mentioning.
A retail price of £20 for a Immobiliser/Alarm will be from the far east and the quality will be suspect
Always pay attention to making good quality connections, twisted wires and tape is a fire hazard and dangerious
Your introducing connections and components into the wiring which could be the source of trouble
Obviously there are better quality systems out there which cost 10 times the money which work and are insurance approved.
But I'd rather see a hidden switch on the coil - than all these cheap systems. I have a rubbish bin full every year ones that go off in the middle of the night all the time or breakdown on the side of the road.