Yes, there are statutes of limitations involved. While New York law does not directly impose a statute of limitations on traffic matters, there have been successful motions to dismiss based on failure to prosecute and speedy trial grounds.
I have done it myself. I appealed a speeding ticket issued in Bedford Town Court to the Appellate Term, Supreme Court and won.
Provided that your boyfriend remitted the ticket with his "not guilty" plea when he was supposed to, has not ignored appearance notices or has not taken steps to conceal his location, he has a very good chance of getting this dismissed, perhaps not at the trial level but definitely on appeal.
There is plenty of case law to support a motion based on failure to prosecute.
The Appellate Division, Second Department has ruled that while no New York statutory speedy trial protection exists in traffic law, there is a constitutional speedy trial right that applies to all prosecutions, even in traffic matters.
Under New York law, the prosecution must be ready for trial in 30 days for violations, 60 days for misdemeanors, 90 days for Class A Misdemeanors and 180 days in felony matters. Traffic matters are considered as lower to, or equal to, violations.
Speeding violations, while technically traffic matters, have been held as being the same as criminal matters, as jail time is a possible consequence, thus deserving of all CPLR and CPL requirements & protections. Therefore, some New York courts have held that speeding matters must be ready for trial within 60 days. Three years is far too long.
If you wish, provide an email address and I will send you case law and a copy of my appeal brief.