Yes that should be no problem to write to it continuously for 2 weeks.
If your API allows it, there may be a way to "force" writes out to the card, so they aren't held in cache for too long, where they would be lost upon power off. I ended up writing every ~2s and forcing actual write every 30s or so. If power is lost then at most I saw that 30s of data gone.
I was using Fatfs: f_open, f_seek to end, then f_write, and f_sync to force writes.
You might consider creating a new file every day, with current date in the name. That may reduce the chance of corrupting one big data file, and limit loss to a single day (but I never saw this happen).
Also, make sure you are appending data to the end of the file, so if the program restarts it won't overwrite data.txt accidentally.