While many players and GMs really don't like romantic character arcs or are in it just for the comedic appeal of flirting around a gaming table full of buddies, there are some who through personal interest or a strong ability to suspend disbelief can really get a lot out of it. This can be especially true in solo campaigns where there's more space and time to delve into a single character's personal interests. Especially since romantic sub-plots tend to develop more readily and naturally between a PC and an NPC than between PCs - likely because players are closer to their avatars than a GM to one member of a giant cast.
However for those who have delved into romantic sub-plots, they may have noticed the same issue arise that does in television series world-wide. Once the romance is consummated, either by marriage or in some cases sex, the interest in that interaction slowly starts to fizzle.
The reason for this is that Conflict = Story and thus the very conflicts that had driven the romantic angle, once resolved, pushes that interaction further and further into the dull downtime space of the tale. After all, you don't play out the other elements of mundane existence or, if you do, they're treated as a prelude rather than the main event.
The fact remains that the clearest and most driving motivation of a romantic sub-plot (the "Will they?" "Won't they?") angle can raise its head the moment two characters hit it off. Once it has been resolved that "Yes, they will," you're stuck trying to figure out where to go from there. So firstly I'd recommend that you play around with that tension for awhile. You don't need to go to ridiculous lengths to keep the two separated (i.e. like many television shows) but if there are valid reasons for the two to dance around each other, do so. The flirting can be half the fun.
Afterwards you can't rely on flirty tension to keep the story thrumming for very long. Instead you need to find more character questions to ask. The most obvious is the civilian / adventurer spousal conflict, but that can pale pretty quickly and make the civilian look like a jerk ("Sorry I missed your birthday but I just went through level drain to save a village from the undead that would have converted them all"). This could be improved if the civilian had to cover for the player character, as at least then they're an ally. Sure this removes the tension from between the two characters, but that's fine. All you need is to involve them in "a tension" or "question". Mediation certainly works.
If they're an NPC Ally, there's also the temptation to have them kidnapped or put in jeopardy, which can work once or twice but afterwards gets old and staid. Of course having them save themselves while the PCs are coming for them, or having their apparent kidnapping being staged while they're actually out shopping, can certainly make for a change of pace.
Finally if they're part of the adventuring party, consider using non-romantic tensions that can come up with any party dynamic. What if one wants to take prisoners and the other doesn't? What if one craves revenge and the other doesn't see the point? What if someone flirts with one of them? How does the other react? Think about the kind of spice you might add if the player had selected a spouse as an NPC at the start of the campaign. How would you keep them relevant? What would you do to make them interesting?
Hope that helps! If you've ever included a longer running romantic arc in your campaign, let me know how you kept it interesting in the comments box below.