Although "maybe" looks like the words "may" and "be", it functions separately and differently, just like "however" is not "how ever".
It is also phonologically different. Maybe is /ˈmeɪˌbi/ with stress on the first syllable. May be is /ˈmeɪˈbiː/ with equal stress on both syllables. So we can clearly tell the difference between the two in spoken English.
"Maybe" is related to "may be" the sense that the pattern:
Maybe [clause]
can usually be rewritten, and can perhaps be regarded as a contraction of:
It may be that [clause]
The "it" is a place-holder subject, just like in "it is raining" or "it is said that ...".
"Maybe" is a fairly flexible particle which applies to entire clauses ("Maybe I should wait"); verb phrases ("I think he maybe went home already"), adverb phrases ("I can finish that in three hours, or maybe sooner"); adjectives ("I don't remember what color it was: maybe red, maybe orange"); or nouns ("I see a vehicle in the distance, maybe a bus, coming this way"). "May be" cannot be in the same way, simply by placing it in front of a clause or phrase. It is a compound verb which requires the formation of a clause with a subject. If we replace all these uses with "may be" we have to rearrange or complicate the sentence so that there is a proper embedded clause built around "may" with a subject: "It may be that I should wait"; "It may be that he went home already"; "I can finish that in about three hours, or it may be that I can finish it sooner"; "It may be that it was red; it may be that it was orange"; "I see a vehicle, which may be a bus, coming this way".
And so,
Maybe it's time to switch doctors.
can also be expressed as
It may be that it is time to switch doctors.
possibly even with the complementizer omitted:
It may be it is time to switch doctors.
But "May be (/ˈmeɪˈbiː/) /it's time to switch" is not grammatical. The verb "may" is lacking a subject.