It took Turkey a very long time to officially accept that there was a Kurdish minority in that country and to recognize them as Kurds. Turkey used to label Kurds as 'mountain Turks' and tried to assimilate them by destroying their ethno-cultural identity and language. Thats pretty much the crux of where all else eventually resulted in the armed revolt by Kurds against Turkey under the PKK.
The conflict has worsened in recent years because it has now spilled over into Iran. There has been some Kurdish discontent in Iran since the early 20th century, but nothing on the scale of what Turkey has had since the 1980s. But now the PKK has broadened its movement to include Iran too where it operates under the name PJAK. Before in Iran, Kurdish opposition revolved mainly around Komalah which was a Communist movement, and PDKI which was Kurdish nationalist group. Both of these had an Iran-orientated agenda, not a pan-Kurd one.
So given that now Iran also has been brought into the larger Kurdish movement that started in Turkey i would say that Turkey really needs to stop denying that this conflict is dying down, because it isnt. Its getting worse. Just within the past month or couple of months like 50 Turkish soldiers have been killed. Pretending that Kurds have no popular grievances is self-defeating.