Both Alice and Bob are asexual, but not aromantic; they prefer to engage into other kind of amorous interactions not related to intercourse.
Despite being married Alice and Bob have decided that they aren't ready to have sex yet.
Bob and/or Alice aren't/isn't comfortable having sex because they've/(s)he's experienced sexual abuse and can't help but be reminded of that experience during sex. So they agree not to.
Bob and Alice have analyzed the very idea of sex, seeing it as bad from a logical standpoint (S.T.D.s, touching organs that pee & poo, vaginal pain if the penis is too big, etc.). So in-order to maintain the idea that they are more logical than everyone-else or simply just because they think it is rational, they decide to refrain from all sex even if they really want to.
Bob and Alice want to study each other's sexual preferences and what makes good sex so good first, to make sure their first time together is enjoyable.
Alice or Bob has A.I.D.s or some deadly S.T.D. or S.T.I. and (s)he doesn't want to risk his/her partner's safety.
Deconstructed: Abstinence from sex can put a strain on the relationship, especially if it wasn't by mutual agreement. (And if it was, then one or both of them may not be up to the challenge.) It may also be a sign of personal or relationship problems, and may lead to cheating or divorce.
Reconstructed: Alice and Bob are no longer in love but still like each other as friends, so they stay together.
Played For Laughs: As a Running Gag, Alice asks Bob if it's time to finally push the beds together. Bob invariably replies, "Not tonight, honey."