I did check your service package and you are able to set up 24/7 recording. Below is a guide that shows you how to set it up. I believe it should should work with other brand SD Cards but the reliability is where it might have some trouble. It needs to be an SD card made for continuous video recording which could burn out a standard SD card after a few months. I would imagine Reolink SD cards can handle this. I will ask Alarm.com tomorrow and let you know incase there is a known issue using Reolink SD Cards.
Can you try disabling the rules and then re-enabling them as well as performing a power cycle by removing power for at least 2 minutes and then powering back on.