Time on an 18X without an external clock or pauses? You can't.
Well, you can, if your code takes a defined time to execute and I've used this technique before where you write your code perfectly, then put it in a loop, then run the loop 10,000 times, measure it using a stopclock and work out the time per loop. The catch is that every time you change just one instruction you have to do the whole thing again.
You can use an 18X and a DS1307 external clock.
You can use an xtal module and a single binary counter IC chip with a reset input. Lots of options there, as you can use an output from that binary counter to to an interrupt on a picaxe.
I still don't understand what you are trying to do. If you don't build your low pass filter properly, the error due to Nyquest etc is going to be 100x the error that you would get from a timing error of 2 secs +/- half a sec. So you could spend all your effort on the perfect timer for no real gain. What is the signal?
Also, ok pause is not doing anything, but what were you going to do in that time anyway. Were you going to sample the signal more often? Ok, sample it more often and use shorter pauses. Sample it so often that there are no pauses, and then see how many times you loop through the code in 2 secs. Multiply that loop counter by 10, do it over 20 secs or 200 secs then work out the error and you will be able to get it very close. Unless of course you are doing other things in the meantime, in which case, what are those things.
You may still need that low pass filter though.
And hippy is right. You might not need a picaxe at all. Use a cap and a resistor as a high pass filter. Run that into diode and then an op amp voltage follower and then a RC network. But I wouldn't suggest that until we get more info. Are you interested in detecting the number of high pulses, the magnitude of the highest pulse, the average of all the high pulses, the average of the high pulses over a certain threshold etc? Too many questions...