You should stay online when you’re available for work. You should never be online when you’re not, actually, online.
That means no tricks, no plugins to autorefresh (which can get you banned!). I always carry the app with me to answer any messages or requests on the go, and I keep the website open while I’m in the studio/office.
When I’m offline, I’m offline. There’s no “set time” you have to be online every day. But often, I’ll find myself contacting sellers who are indeed online (filtering out the offline ones), so staying active and online is absolutely important. But that also means that you have to be available to answer any messages quickly! If you’re “online” but in fact, are not available right away, that will just annoy the buyers, and not get you any more business.
Keep in mind that you may get banned with using any tricks to stay online while you’re not actually available, so don’t do it.