For experiments which are "very expensive" and "samples" it would be foolish to save a 3 yr old Methanol bottle to ruin all experiments. Without a second thought, but a lot of new bottles of LC-MS-Grade Methanol.
Biswapriya's advice is the most sound to follow. You get all kinds of leachates from the silica or plastics used int he bottle and caps over time that can adversely affect things. Note, acetontrile goes bad for MS use even before the expiration date, even in an unopened bottle. We found that we had to chromatograph even LC/MS acetonitrile through neutral anhydrous alumina. This can be stored sealed for about 2 months before it needs to be done again.
Part of any valid experiment is determining the suitability of reagents used. Run a method blank and blank spike with your methanol. Were there interferences? If not then it is suitable for use. You would have to do this with new methanol; you already own this methanol.
I'm not sure where you came up with an expiration date of 3 years for methanol; certainly no manufacturer that I am aware of would publish such a date.