Pen battery-life vs. disconnect?

So my stylus has gone through two AAAA batteries in the past because I thought that it ran out of power each time it stopped responding to my surface. And each time it happened the recovery time took a lot longer, so I was just replacing the battery. I thought I was able to predict it by how long I could use the stylus (during a drawing) before it crapped out and it lasted only a full day's worth of drawing.

As it turns out, the recent time this weird disconnect happened with my current battery, the stylus was still fine days after. Does anyone know if the stylus just loses connectivity to the surface and takes a while to reestablish? Or is it really a battery-related issue?