The pop-up plugs on bathroom sinks tend to loosen up over time and lose their watertight seal. As a result, water trickles down the drain, making it impossible to keep the basin filled up.
You can fix this annoyance in less than a minute. Look beneath the sink and locate the large retaining nut that secures the horizontal pivot rod to the back of the vertical drainpipe. Grab the nut with pliers and carefully tighten it.
Pull up on the plug handle and turn on the water to see if the plug seals tightly against the drain. If it doesn't, tighten the nut some more. If you can't raise the handle, then the nut is too tight. Loosen it a little and test the plug one more time.