Is there any way to reload a modprobe module once every certain period of time?

Create a cron job to check the connectivity every 1 min.

sudo vi /etc/crontab 

then add the following line

* * * * * root /usr/bin/ping -c2 8.8.8.8 || /usr/sbin/modprobe -r ath9k_htc && sleep 0.5 && /usr/sbin/modprobe ath9k_htc