When we talk about the two-body problem, we talk, mostly, about that nuclear relationship and what it suffers as a result of two jobs in two locations: the time, expense, and hassle of commuting; the deferral of child-bearing (or the exponential explosion that is the three body problem); and the general emotional strain on the partnership.
What gets less discussed--I'd say never discussed, but I guess I haven't read every last thing on the internet--is the strain on all the other relationships to which either partner is a party. Since we've just concluded one major holiday and are fast approaching another, let's talk first about how a long-distance relationship complicates familial relationships.
Now, as long-distance relationships go, Cosimo and I have it pretty easy: we don't have kids, we're close enough to see each other every weekend, and both our families are happy, healthy, and financially stable. Still, we want to see each of our families at least twice and ideally three times a year, and since each lives a full day's journey away, there's no such thing as a weekend trip.
Many couples these days live far from either partner's family, and face logistical problems (or familial conflict) as a result. But when a couple lives apart at least half-time, the logistical and familial issues can be close to unworkable. If the couple doesn't even see each other often enough, it's hard to sacrifice their already-limited time together. If one or both partners are spending significant hours on the road or in airports just to maintain their relationship, they may resent the idea of spending even more time traveling. And if they have a primary home that one partner doesn't live in full time, it's hard to give up holiday or vacation time there.
Friendships present a similar problem. It should be easier to maintain independent friendships in a long-distance relationship--no need to make excuses for going out with the girls/guys; for seeing that friend your partner can't stand; or for seeing one-on-one that friend your partner would be hurt not to be seeing as well--but in practice friendships often get sacrificed: the partner who commutes has little enough time to attend to all his or her work obligations (and keep doctor's appointments and sit at home waiting for the cable guy) between packing and travel days, and both partners may be jealous of their weekend time together and socialize less than they otherwise might.
So far, the best solution we've come up with is to pile everyone in the same place as often as possible: each of the last four years, we've had an Autumn Weekend of the Parents, where both sets come to visit us (helps that our parents get along!), and we're devoted to the dinner party (such an efficient way to see multiple friends over multiple hours) and the occasional weekend get-away with a gaggle of our beloveds.
It's still not enough. It's never enough. (But better, I suppose, than the opposite problem.)