Eb3a plug in AC120v 24h/day

I use this EB3A, basically for my Cpap Airsense with draws power about DCv 24V 2.71A when running, and I use the Cpap about 8hrs/day.
I want my Cpap always on 24h/day.

If I plug in AC120v 24h/day, would kill your battery cycles(batt life time) because charge/discharge all the time ?

Please advise me.