First, racism - real racism - still exists. We have made much progress since my childhood 50 years ago, but it is still very real - and it infects some people in ALL RACES. The biggest difference is that it is no longer socially acceptable or widespread.
Second, as has been mentioned, pulling the race card is a very effective way to marginalize someone the left does not want the public to listen to. Thankfully, they are over playing it and it is less and less effective. It is also rendered less effective by the ever increasing number of Black and Hispanic conservatives.
Third, the biggest reason that the race card is constantly played is that there are many people invested in the "race problem" continuing to exist. If racism really is getting better, than many people are at risk of loosing political power and others are risk of loosing their living and their lifestyle.
There are some similarities with the war on drugs - millions of people are dependent upon the war on drugs continuing, even it it accomplishes little to no good. The same is true of the "war on racism" - the day it is won, the "soldiers" will be unemployed.