when an alarm goes off, I deactivate it and then I can't reactivate it,
By "activate" and "deactivate", I'm guessing you mean Arm and Disarm. Your phrasing makes it sound like this has happened more than once, but if that's true, then you must have been able to Arm it more than once, so are you able to Arm it after waiting awhile? Or did I just not understand you?
Fire alarms and Intrusion alarms are different things, treated differently. I'm going to assume you're talking about an intrusion alarm, which can only happen if the system is Armed.
What zone triggers the alarm, and what is on that zone? Read your User's Manual to see how to access the Alarm Memory and see what is _causing_ the alarm to begin with.
User's Manual:
https://cms.dsc.com/media/documents/all/PC4020_v3-2_UM_EN_NA_29005036_R001.pdf
Full disclosure, it's probably been close to 20 years since I worked on that model---but typically control panels of that era (and after) will not let you re-arm after an alarm, until after you've cleared the Alarm Memory; and then you can re-arm it. Check the User's Manual to see how.