Are the Kindle’s days numbered?

I still have an older model of the beloved Kindle reader, the kind with the black and white screen and no backlighting. I can still download and read books on it and browse the web, so it still works reasonably well. The only thing I can’t do is hook it up to Facebook. Each time I try linking my Facebook account, I always get the “Web browser is unable to establish a secure connection with this web site.” A search on the web for a fix to this problem yielded no results and I checked Amazon for any Kindle updates that could possibly fix this issue, but apparently Amazon is no longer concerned with keeping its older Kindles up to date. I fear that these older models may be reaching the end of their support cycle. Too bad. As tempted as I am to switch to one of the newer Kindle models, I do not see myself parting with the classic model I already have. I still enjoy it too much to even think of getting rid of it.