What I found with mine was that the power converter (inverter) was in an overtemp mode and was basically shut down and trying to restart. It was going from 11.5 volts to about 13.5 volts for about 10 seconds every 3 seconds or so. In the power supply industry this is called hic-cup auto restart mode.
The root cause in my case was that the power converter was always starting up at 14.5 volts which is not correct except in an extreme discharge situation which you seem to have. (My battery was at 100% charge).
I replaced the power converter section and my problem is gone.
My guess is that you will be ok if you disconnect your battery between uses. My battery is on charge virtually 24/7/365.
The power converter actually has 3 modes of operation to allow for continuous chargeing.
Here is a link to a very detailed description of how the converter should work.