A couple of questions first.
Were you saving your work just to the NAS or is it on the PCs hard drive as well?
Are you using the NAS as an external drive to your PC and assuming it will also act as a backup? There is a very big difference between the two (we use several NAS boxes as direct backup to our PCs hard drives - backup every 10 minutes - those boxes are then backed up overnight to other NAS boxes and our storage system).
If you were using the NAS as an extended drive did you call up any of your work from the missing 10 days? If you did and you could read it then it is most probably there unless you have the RAID 1 set to automatically rebuild in which case it MAY be 'gone' but recoverable.
Now to try and solve the problem, or at least not make it worse.
First, remove the possible failed drive leaving the 'good' drive in place (power off the unit to do so and while it is off give a visual check of the inside for fluff build-up or damage).
Now you use the 'failed' drive to practice on. Get a USB/SATA caddy or powered adapter and install/attach the drive. Assuming you are using a windows PC you can either download the software listed in the recovery sticky (Ext2IFS works best on older windows systems - R-Studio and NAS Data Recovery work on all versions of windows from XP but cost money) or follow the Additional References link and use a Live Linux CD.
Which ever route you decide to take you may, or may not, see any information on the 'failed' disk. You can also download the disk manufacturers disk test tools and use them to test the disk to find out its actual state - good, bad or indifferent.
Because you set the drives up as RAID 1 you should be able to power up your NAS and use the files on the remaining disk as if both disks were present. You may find your missing data. If you have problems doing so there may be a problem with the NAS or power supply.
The next thing to do is backup all your data on the NAS to an external drive (it can be 2TB USB drive or an extra disk installed in your PC) that way should anything go wrong you have your data safe.
If you can read and use the data on the 'good' drive, get a new one and install it and allow the raid to rebuild. You are then back at work but, for your own peace of mind, backup your work every night as the last thing you do.
Edit: Cable2 you beat me to it again
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