Very often online surveys begin quickly, but then slow down sharply as they near completion, and ultimately take a long time to finish. They may even grind to a halt before the full sample has been achieved, because there are no more available respondents.
In order to try to avoid these problems the agency running the survey might ask the client for permission to relax or open quotas during fieldwork. Basically, this means allowing people to take the survey who do not really qualify (or who you don’t really want). They might be outside your specified age range, for example.
Relaxing quotas is clearly not ideal, so is there an alternative? Yes, and it’s an easy one. Essentially, all you need to do is ask the agency before the survey begins which will be the most difficult quotas to fill, and which will be the easiest. They might say, for example, that younger males will be the most difficult, and older females the easiest.
So you just agree with them that they will target the most difficult quotas first and the easiest quotas last and, just as important, that they will not go too quickly on the fieldwork. You then ask for regular updates during fieldwork, rather than just leaving the agency to it.
This approach may not completely remove the need to relax quotas on every survey that you run, but it will certainly go a long way. And apart from giving you better quality results, it will also increase the likelihood of achieving the full sample, and reduce the time required to finish the survey.