What is the theme of "Goe, and Catche a Falling Starre"?

"Goe, and Catche a Falling Starre" is a rather cynical poem expressing the view that all beautiful women are unfaithful and false. This is of course a misogynistic, bitter, and irrational complaint, likely motivated by the poet's own misfortunes with women.
The speaker says that one could wander for "ten thousand daies and nights" and never find "a woman true, and faire." In fact he says that such a treasure would be as impossible to find as it would be impossible to "catche a falling starre," or "heare Mermaides singing." One might wonder, at this point, about the speaker's implication that there is a direct, causal link between a woman's beauty, or how "faire" she might be, and how faithful or unfaithful she is. Perhaps he thinks that plain, less beautiful women are capable of the faithfulness which evades their more beautiful counterparts.
In the third stanza, the speaker says that if one were to find a woman that seemed true, she would inevitably prove "False, ere I come, to two, or three." This false, unfaithful nature of beautiful women constitutes the primary, ostensible theme of the poem. One might also say, however, that the implied rejection, or rejections, and the consequent bitterness and cynicism of the speaker, constitute the implicit and far more interesting theme of the poem.

The theme of John Donne's poem "Goe, and catche a falling starre" is bitterness at a love betrayed. The speaker invites the reader to try doing impossible things, saying that even if the reader succeeds, there is one impossible thing they will never do: meet a faithful woman. Even a woman who appears faithful will show herself to be false, given enough time.
To catch a falling star, or hear the singing of mermaids, is as unlikely to the speaker as "keep[ing] off envies stinging" or discovering the means to "advance an honest mind." The speaker feels he has been poorly treated, despite being "honest," and not even someone gifted with psychic powers could give him proof that his bitterness is unwarranted:

If thou beest borne to strange sights,Things invisible to see,Ride ten thousand daies and nights . . .Thou . . . wilt sweareNo whereLoves a woman true, and faire.

A faithful woman is more mythical than the powers of the mandrake root. Should the reader succeed in finding one, the speaker would not go to meet her, for all women are only faithful for a time, before giving their love to others.