I think there's a LOT of implications by asking that question -- some may be true or have more influence, some may be less true or have less influence. Such as:
1a.) Sabres' development system is sub-par
1b.) Sabres' organization and/or coaches do not know how to get the best out of players
2.) There is more pressure on the players to end the streak than the general public is aware of (some of that may be self-applied), and some/many young players fold under that pressure or at the very least do not perform well under said pressure (As an aside to that, I think it should be noted that few older/veteran players play well after leaving Buffalo....it's mainly the younger guys that flourish upon leaving)
3.) The front office hasn't been capable of surrounding the youth with the correct vets or the correct type of vets
4.) The front office/organization hasn't been patient enough with the young kids before "giving up" on them
5.) The front office/organization has identified the players they want to build around and have chosen poorly
I do NOT think that players are intentionally playing poorly to get to where the palm trees are. I just don't think that many NHL players have that type of thing in their DNA. Sure, maybe one or two tanked it to get out of here (Berglund, I'm looking at you.....with a side-eye to Taylor Hall)....but I certainly don't think it's a common occurence.