Most of the time I'll just gradually fall out of interest in a webcomic. I usually juggle a great deal at a time, there aren't many I'll follow weekly because doing that one page a week just isn't that pleasant in most cases. Everything takes so long to progress, I'd rather wait and read it later. Shoddy updating schedules and a complete lack of communication from the author is one big thing. Dropped one of my all-time favorites, Lumine, for that reason and more. Only so many unannounced hiatuses and with zero information or update about anything I'm willing to put up with before I cut my losses and move on. Judging by a lot of the comments over there, I'm not the only one.
I have a personal system where I'll give comics about six or so months to update before losing interest and moving on. With different time-frames depending on my interest. I.E. I'm basically never giving up on Serpamia Flare or King's Folly 'cause I hold those comics in extremely high regards. That's a big reason why I eventually lose interest in comics. Six months is the minimum though; I nearly always extend it further if there's a reason. I.E. Comic says it won't start up again 'til Summer, I'll give it 'til Spring of the next year to update.
For comics I'm reading but not too sure about: any number of things honestly. Could be I don't like certain characters (seen some comics that have some characters I hold in the same regard as a Giant Praying Mantis with the head of Joseph Goebbels), certain scenes or plot-lines I find asinine or distasteful (any comic that says "You kiss someone, you gotta marry them" is an insta-drop for me for instance), or it feels... soulless. Premium comics I'd read always had that issue; they rubbed me the wrong way, like they weren't made out of passion or fun in the slightest.
Forcing a romance until its hollow, rape-scenes, rape-scenes trying not to appear as such, romanticizing or normalizing abusive characteristics in relationships, cliche characters that don't go beyond their cliches, and extremely, ungodly, sickening violence and Grimderp are all reasons I've dropped comics in the past. There was one... oh my God. From a WH40k nerd, it was such a good story, but the level of graphic violence was life-altering. I felt dirty inside having read it. Jesus Christ in Heaven...