Security light on console staying on solid running battery down

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The security light on the console that normally blinks when the car is locked, stays on solid. The car cannot be remotely locked and this runs the battery down to the point where the car will not start. I can re-charge the battery which resolved the problem for a short while, but the issue begins again. Am told that the problem may be the security module, but don't know why when the battery is re-charged, the problem goes away for a short period.