Your SSD should be able to stand being run for long periods of time. Conventional wisdom is - HDD = spinning disk = more likely to fail over time; SSD = no spinning parts = less likely to fail over time. Of course, you already know this. That's why you bought the SSD in the first place!
There are always exceptions to this HDD vs SSD rule, though, so backing up your drive isn't a bad idea. I speak from experience, since mine recently crashed with 4 years of invaluable college course work on it!
To answer your question in a nutshell, never shutting down your hard drive isn't harmful for a short amount of time (days), but could be harmful over a long period of time (years). Again, you've got an SSD so I wouldn't be all that worried about it.