Are you sure you are motivated? Motivation in a general context is one thing which I'm sure you have (you look very motivated in your profile pic, lol), but motivation at the focus/ goal level might be lacking for you. Exogenous circumstances become irrelevant when training is goal-oriented, or if there is a laser-precise focus. If rain bums you out then maybe whatever goal you have is not strong enough to carry you through at this particular moment in your day/week/life. It is usually a sign to do something else instead and wait for inspiration or motivation.
As someone who used to run in every weather condition, I ran because I wanted to get better; but, once I became satisfied, for a time, with my skill level I lost the motivation to run when I didn't feel like it or during rain. Besides, with running it is best to listen to your body. It is like losing weight, the greatest motivation to drop poundage is fashion and sex, not health and fitness. Maybe you just need to find a very specific motivator that is unique to yourself.
Or, all the above might be wrong and you are suffering from a very relaxed nervous-system. Apparently, the more you train, the deeper into "relaxation-mode" the nervous system spirals and this causes a prolonged period of "fuck-it-all" feelings So, if you wake up in the morning and you are tired/lazy then that may be a sign that you just need some time to rev up your body. I know many people who usually need about 3 miles before they feel good. I, personally, need about a week.