Well it was a 4-year-long war, wasn't it?
We don't know for sure. It could have been 4 years. It could have been 54 years. It could have been 4 weeks.
The relative lack of information our heroes have on the particulars of the war might suggest that it was a short and relatively insignificant skirmish. "BoT" doesn't paint it as having any modern relevance - the only reason the issue comes up at all is because the ancient war resulted in this silly Neutral Zone that Starfleet still is forced to observe and enforce, and the only person aboard with an initial personal connection to this conflict is Stiles. Even the later episodes tend to describe the old war as having been relevant only to the Romulans, who can't get over it even after 200 years; the Feds don't have similar passions.
On the other hand, the Romulan side does opt to emote over the fact of how bitter the war was - and to this day, we don't know who won it. So it could have been an affair that dragged on for decade after decade, until both sides got so fed up with it that they decided upon this Neutral Zone that both sides hated but that was still better than persisting with a hopeless quest for victory.
Four years or shorter is a neat package if we want the war to be over (and perhaps forgotten) by the time of "TatV". It is also a good choice of length if the war starts after "TatV" and ends before 2166-67 which is the "it happened over a century ago" limit. The third possibility of course is that the war was already fought before ENT began (and the identity of the enemy was only discovered, and the concluding treaty made, later on), but I doubt anybody would want to take that route now.
And the fourth possibility is that the war was ongoing during the ENT adventures or "TatV" but went unmentioned. This is what happened with the Cardassian War in TNG, after all. Or with the Klingon conflict in TOS before "Errand of Mercy".
Personally, I actually like the fourth option the best. The old chronologies speak of the war starting in the early 22nd century, but they also speak of it starting with the mysterious disappearances of Earth or ally vessels, colonies and installations. This may well be what was going on during ENT, a show that tells us that ongoing piracy against Earth vessels was the norm of the day...
Timo Saloniemi