Yeah internet connection can be like that for PvP if its not great or starts becoming unstable at times where it can even affect DQ. Don't worry about grinding much as the cause as it doesn't take a toll on internet just to search opponent and convenient that arena battles are offline until the match ends anyway but it will still use some internet.
Basically playing when you think you can is fine at a good time of day or best connection or manageable and when things get tough with connection, you can take break, try again, find a better internet spot or more. Whatever you feel works best basically.
I used to have DQ arena connection issues and it was annoying that my internet was once not stable or good enough or random disconnect (low signal can be a bad habit too). I don't face this as much anymore though but once in a while such as when I need to restart the game and only then I connect to internet.