Yes, you are right. Those were just rumours and I misread a headline. Actually their 'minister of defence', Moroszov, just claimed to hold a
part of that airport.
Yes, the airport has been under attack multiple times over the last month, but according to the press-center of the ATO, this is a new wave of attacks including mortars, tanks, artillery and Grad launchers.
http://korrespondent.net/ukraine/pol...tska-shtab-ato
Apart from that, Ukrainian positions are occasionally under artillery fire also elsewhere, but not as intense.
This airport seems to be really important to the separatists and from what I know, it is also the last Ukrainian foothold in Donetsk. It seems that the separatists plan to push Kiev out and the afterwards consolidate their power in the status quo. However, they risk the ceasefire in doing so, although I doubt that a new escalation would be in Kyiv's interest.