This article seems to be targeted at tinkerers, who are likely to have at least one device in their home running an HTTP stack that is available on-demand. Running a 24 hour server needn't be expensive; The Photon (Sparkfun Core,) Arduino, and even Pi can be powered with very modest current draws.
I just started playing with my first Dash button recently, but I ran it through about 300 cycles, and the battery is still going strong. I get the feeling that your 2 month estimate is undershooting what the dash and a AA battery can get done. If it really came to it, the on-board LED can be bypassed for some power savings.
The Flic button is something I'm looking at also, but it's not a replacement for me; You can only pair the Flic with one device (phone) at a time. For me, that's a deal breaker. If I'm just out of range, and my girlfriend would like to use the Flic button, she's out of luck. Unless I share the button with her, and she sets up the actions for her phone.
This is one scenario where a central server is beneficial; If we have a lightweight device listening for button-presses, that server is a one-stop-shop for programming buttons. And if I administer that device, I most likely have access to my personal libraries and APIs, instead of being limited to whatever Flic, or whatever the company may be, approves and exposes.
I would love it if Flic would support and encourage more open-source development.