Why would a gym ever be left undefended?

There are 6 gyms in my area and every once in a while I will see that one of the gyms is completely undefended, which allows me to claim it. Why would this happen? In all the cases this has happened I looked around and no one was around, so I don't think anyone was in the process of claiming it before I did. Are people defeating gyms and then just forgetting to claim them?

Some of my friends leave conquered gyms undefended because, at least where we live, gyms are un-defendable. Trying to defend just leads to a loss of potions. So, we go out on marauding missions and destroy gyms. Our calling card is that we leave it undefended (or have Pikachu be the defender). I just did this last night! :-) I've heard others do this to maybe send a message to Niantic.

As you said, this is entirely possible. It could also be:

• Someone beats the gym with their last available pokemon, and has no way to revive their current pokemon.
• Their game may have crashed after taking a gym, and be unable to play
• May be due to bugs and issues

There is no tactical reason for this.

I don't see a reason to leave a gym undefended either.

There are a lot of factors that could stop you from claiming it though:

• Public transport: Maybe you can start a fight but move before you are able to claim the gym
• Running out of potions: The only requirement for a defending pokémon is 100% HP
• Server, GPS or battery issues...