BLS-2014 is still available for download/updates, and the product life cycle indicates that its end-of-life is 5/31/2017.
I still have BLS-2014, so I attempted...twice. For this, I used BLS-2014 26.06.07, although I do know that a newer version 26.07.01 is available. With the version I had: The upload goes through the process, but no e-mail comes in saying the upload is complete. On the home page of leaguesecretary.com, the league name does show...but in my case, when clicked, went to the most recent upload as done with BLS-2017. I first attempted an end-of-season for April 2014, then I restarted that league with a start date in September, 2016...still, no dice. There's an outside chance that the newest BLS-2014 would work, but I highly doubt it.
The file structure changes from season to season and there comes a point where leaguesecretary.com has to update its processes to handle the revised data format from CDE...and with that, comes an inability to process something from an earlier version. Whether it can go back one year or two, I would suggest that depends on how significantly changed the aforementioned structure is.
To further update: I received an email saying that the upload from BLS-2014 had gone through (I knew it was from last night's test) about 13-14 hours after the test. However, the current season upload (of the same league, it's an active 2016-17 league) shows, because after the test, I re-did the upload with BLS-2017 so that LS would display the correct league information in the end (for practical purposes). In short, it does not appear that BLS-2014 is supported by leaguesecretary.com.
Always check, download, and install the most recent update of your software to ensure that issues may have been corrected.