Code flow for precission applications
Yes, in theory you can always miss events if you use a polling approach like that. Whether or not that's a problem depends on how accurate/frequent your data collection needs to be.

You can often mitigate the issue to an acceptable level if you are able to poll fast enough. That's determined largely by what else your main loop is doing. The more work it has to do elsewhere, the longer it will take between calls to analogRead() (and the more likely it is to miss something). Optimising your code can help.

You may also find that you can compensate sufficiently by interpolating between samples. Linear interpolation is very easy, although more complex options may also be possible, especially if you're processing the data offline afterwards.

If polling isn't working for you, then interrupts are the obvious alternative. Since you're reading an analog signal, you'd probably need some external circuitry which does a voltage comparison. You can get dedicated comparator IC's from all sorts of vendors, or use an op-amp circuit if you prefer.

If the signal goes over a pre-determined threshold, the comparator would have to pulse or assert a digital line. That could trigger an external interrupt pin on your microcontroller, which will execute custom handler code. See attachInterrupt() for more information.