If the flash drive fails, yes you can continue to read from it, but you also have to consider what is meant by reading.
You can always read the raw data from the device, that will never change. There is nothing that prevents the electrical signals from forming a proper read transaction on the IO pins of the flash IC chip.
However, when you consider the software that is on top of the raw data (a file system for example), this is where you will have the trouble.
With older CF cards, the concept of wear leveling was not implemented, I don't know about newer ones. This being the case, the directory structure for a file would more than likely reside in the same physical location on the flash. Opening, writing, closing a file with the same name would no doubt wear that space out as the directory entry gets hammered. Once that has "worn out", data is lost because the file system can no longer track it (even though the actual data may be viable).
Also consider the device that does support wear leveling. At some point it will run out of places to wear. Some large files will remain static and won't move (they are only read), some files will be moved all over the device by the device's ASIC as the data in the file is updated or changed. At some point, the flash will run out of cells. This could happen as some critical directory entry is being updated, and the whole file system could be corrupted because there are no more viable flash cells to use.
Your data might still be there is all its binary glory, but w/o a viable file system data structure to access it, well, you're toast. Unlike a harddrive that burped and lost a few bytes, a worn out flash drive has no recordable medium available to do any file system data structure repairs.
Kevin