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Can data be recovered from SSD's?
Can I use regular data recovery software to do it?
It's very difficult I think because of the way data is accessed. The firmware of the drive sits controls access to the actual storage and will move data around to free blocks up on the drive without any interaction from the user. Also because of the nature of the storage itself it is less suited to recovering data. With a magnetic device there are traces left even after the data is overwritten which is not the case when you're talking about silicon.
These issues have already made the work of forensic technicians much more difficult in particular because as soon as they are powered up they will move data around.
There has been some work done on disassembling the drives and reading each chip individually. In this case you will get back fragments of different files which might, or might not, be so useful.
For better or worse, spinning hard drives tend to fail slowly. Ie, once the drive starts giving problems you have a perhaps small period of time before it is dead. SSDs seem to fail instantly, ie, they will work just perfectly, then, not at all.
I know in this case it is too late, but, for future readers who might not have a failed drive yet... When you choose not to backup the data, you have made a cost decision about the value of that data. It's always better to make that decision up front and make it explicit. If you think everytime you save some data to a disk that is not backed up "I'm happy having this deleted at any time" and are content with that decision, all is good. On the other hand, if the idea that the data could be deleted at any moment in time bothers you, you have just answered the question as to whether a backup is necessary or not.