Can I suspend my account, say, for a few months without closing it and losing my number?
Not really! One thought is to switch to the cheapest plan. 1.0 & 2.0 plans can be as low as $5 or $10… 3.0 plans lowest is $15.
If reducing your service level with Republic to a minimum level as suggested by @bocephous isn’t attractive, you might consider a number parking service like NumberBarn. Sideline also merits consideration. In my opinion neither is worth the hassle if Republic’s $5 WiFi only plan is available to you. At $15/month, I would think differently.
It would help us to better help you if we knew which phone and what plan you have currently. If uncertain of the latter, please open the Republic app on your phone and quote, for us, the words describing your current plan underneath your phone number.