The issue is how hot do various bits of the device get. Continuous current ratings are calculated based on the total thermal resistance of the device to ambient. For short, infrequent pulses the thermal capacity of the device matters. For short repeating pulses, the thermal capacity, the thermal time constants, and the dissipation to ambient of the device all matter. For complicated devices (or critical applications) there may be more than one time constant to worry about (i.e., a 1ms pulse of energy W may be OK because it can dissipate into surrounding silicon and packaging, but the same amount of energy in 1us may fry the junction or parts thereof, because the heat doesn't have time to move).
You can either try to find such data for the 1N4001 (and hope that it's the same from brand to brand), or you can figure that if it'll handle 30A for 8.3ms (250mJ, if you assume a 1V drop), it should have no problem with 3A for 25ms (75mJ).
If you study this data sheet from Diodes, Inc., you'll see that they have charts on voltage drop vs. current (which you need to determine power vs. current, which isn't really proportional to either I or I^2), current vs. ambient temperature which you can use to deduce the thermal resistance from case to ambient*, and curent vs. number of repetitive cycles at 60Hz, from which you can get a notion of the thermal time constant from the junction to ambient. From all of that, you can determine whether you're safe.
But to reiterate -- you should be fine. Look at Figure 3, and figure that your 25ms is less than two full cycles at 60Hz, and figure that they're allowing you more than 20A peak for a half sine-wave. The average current of a half sine wave is somewhere around 0.68 * peak (it's 2/pi or something -- I'd have to calculate it to remember), so that works out to 15A for 33ms. Even being really fast and loose with the numbers, it's obvious that you'll be fine with 3A for 25ms, unless your ambient temperature is way closer to 175C than it is to 65C (see their figure 1).
* Said thermal path is through the leads, see Note 3 to the maximum ratings table.