Looks like he's going.
This is all money related. From what I understand, the Burnley directors have made financial security a priority. After many years of financial gloom, Burnley are now debt free, and the directors don't want to risk this by splashing the cash on new players in the January transfer window. They'd rather we went down with no debt and financial security, than risk spending and creating new debt.
On the other hand, Owen Coyle wants to spend some money on new players / strengthening the team. He believes with this money, he could secure Burnley in the Premier.
One of the more recent directors at Burnley, Brendan Flood, had invested several million of his own money into the club. He would have put more money in, but the recession has hit his Property company very hard -
http://www.guardian.co.uk/sport/2009/apr/22/digger-burnley-matt-scottIt's now up to the other directors to supply the money, though the majority view seems to favour financial security.
Brendan Flood now has no more money available to put in. The aspirations of the manager and majority of Directors therefore don't seem to match, so something had to give.
All in my own opinion (as a Burnley fan).