There is a statute of limitations for charging a DUI. This means that a prosecutor has two years from the date of an incident to file a charge. However, once a charge is filed, the statute of limitations no longer applies.
For arrest warrants, some courts do put time limitations on them. So, a court might issue a warrant and put a time limit on it of three years. However, that does not mean that the case is entirely gone once that time has passed. It just means that after that time limit expires, there will no longer be an active warrant that shows up in the court computer system. You may be able to check with the court clerk in the court where the DUI was filed to see if the warrant is still active.
The DUI case will remain open in a court file until your husband shows back up to deal with it, or is found through some other means (for example, if he picks up new criminal charges in the future, the state court computer system will show that he still has the old open case). In general, courts like it when people come back in on their own choice to deal with something rather than waiting until they get caught.
Your husband should strongly consider consulting with an experienced DUI attorney to weigh his options of whether to come back in to court on his own before he gets picked again up in the future.
Typically what happens with a warrant in District Court is that it will be issued for 3 years from the date of the FTA. Once that 3 year date expires, the Prosecutor will reappear on front of the Judge and ask the Judge to reissue the warrant for another 3 years. This can go on and go one. I would suggest your husband talk with an attorney ASAP. Even though this warrant is pretty old, there is still the possibility that he can get booked on it. There are also other collateral consequences that an attorney would be able to explain that can affect your husbands life.