Cycling is a very time-consuming activity. Compared to running, you probably need to put in three times the amount of time in order to achieve the same level of training. This is why some people regard themselves as "cyclists." It becomes a passionate lifestyle, and the time commitment is never questioned. If you're not passionate about it, then you need to take a break.
One thing that might help is to just keep a training diary. Just keep track of how far you went and how long you were on the bike. I just copy the readings off my Sigma bike computer, and I can go back and tell you exactly what I did on any given day back to around the year 2000. I also keep track of brake pad and chain replacement dates and odo readings, so I can tell you how long various components have lasted before they have either broken or worn out, but then I tend to be kind of at the insane level when it comes to record-keeping.
But keeping a diary also tends to make you feel guilty about missing a day. If you're still intending to do that century, then just go out for an hour or less each day, and record it. When you do the century, you're not going to be doing 100 miles all at once. You're going to be doing three or four 25- to 30-mile rides between food stops. And having a record of how much training you've put in will give you enough confidence that you can eventually cover the entire distance.
You can also try retaping the bars, or buying a small component upgrade, or buying a new jersey or something. That might get you more motivated. But that kind of thing only goes so far; n+1 is not really a sustainable strategy.
Luis