That is a problem with ion pair reagents, and why some people do anything to avoid using them. They don't really wash free, with light to moderate washing, so they remain, and interfere with the chromatography of future runs on the same column even if they're not in the mobile phase.
On the other hand, with vigorous washing, you can strip off the ion pair reagent, and then, it will take a substantial equilibration to get it back to the way it was before.
OK, some practical tips. To use your time effectively, start equilibrating your column while you're doing other things at the start of the day. If you can, program the system to start before you even come in that day. You have to go home and sleep, the system doesn't have to be idle while you do that.
A good rule of thumb, is to do test injections. Inject a standard, twice, and get the same retention time, before you start making injections you intend to acquire data from. If the retention time is shifting, or there are contamination peaks, or shapes are changing, equilibrate more, or better yest, re inject, until the system stabilizes.