Hello,

According to your description, it does seem like it was your opponent who disconnected from the fight.
How long was the wait time you experienced before refreshing the page? In case it wasn't too long, I'd recommend staying in battle, to make sure you don't lose.

Does the issue occur to you often, or is it a one time thing?
In case it's a constant situation occuring, I may recommend the cache clear, and/or using VPN while doing Arena, to better the connection.
If it was, on the other hand, a onetime situation, I'd recommend staying in battle for a little bit longer if it were to occur anytime again in the future. The loading for both sides needs to be done to progress the battle, which is why load time like this may sometimes occur.