Forever if you only cut the flowers off. You need to dig it out if you don't want it.

Agree - more or less eternal, that tap root they have...

Dandelions are a broadleaf perennial that can grow in any soil and are most numerous in full sunlight. In the early spring, new sprouts will emerge from the taproot, which can be 2 to 3 feet deep in the soil. They grow yellow flowers that mature and turn into white puffballs that contain seeds that spread with the wind to other lawns. Even though they disappear in the fall, the taproot survives deep in the soil to start the cycle again in the spring. To keep dandelions out of your yard,Lawn or whatever -- this root has to be killed. -- Use:-
Ortho® Weed B Gon® Weed Killer For Lawns Ready-to-Use2 --. Kills dandelions, clover and other broadleaf weeds
Go to www.0rtho.com for more information

Thank you all I did think that would be the answer I have used grass weed killer this year but it has taken a long time to kill off some of the weeds and it can only be used once a year we have 200Mm of grass so it will take me a long time to get rid so once more thank you all

In the past I have carefully used Roundup on individual dandylions. It will kill a little of the grass around the weed but this probably grows back more quickly than you will take to cover all of your grass. Just use a very narrow spray and target the offending weed.