Now that is an interesting subject. I think i started to write to people online back in 2010, or even before, when there was ICQ and such "talking softwares", and i literary talked to hundreds of people. If we got some kind of connection i would say there are 3 main reasons to stop writing:
1. Getting repetitive - i mean no matter how interesting it can get in time it gets repetitive and boring and either i or he/she will stop writing, real life makes things interesting, mutual experiences, so for me just writing online is limited to time, sometimes it lasts longer, sometimes shorter, yet it will end sooner or later
2. Getting too personal - in time some people can develop feelings, i am not looking for anything romantic online, so when it happens i will stop writing
3. Lack of intensity - i dont expect super intensity in writing, but when i get one message per month that is like too little to be entertained to me and i usually forget that one exists, so i just lose interest. For sure its nothing personal, some people dont have time or inspiration. Sometimes its just goes, sometimes not.