A quick update, with information that may interest others looking for power stations, etc. I'm still "looking into it" and learning, so this is not the final word.

It seems that most products use either lithium or lead acid batteries, and it seems that lead acid batteries, such as the ones used in the CAT jump starter or in the Goal Zero power station, require more regular maintenance. This must be what Chaos referred to earlier in the thread. Without regular monthly maintenance, the battery would degrade and eventually die (or die before it reaches its expected lifespan). Lithium batteries seem to require less in the way of maintenance.

For people who may be away from home for months at a time, they may want to think twice about lead acid batteries.