Robert granted it’s been a while since I worked for a business in the UK, so maybe I just have too much of an American outlook here, although, as the owners are American maybe that is the correct outlook for this situation.
Bottom line FSG or any owner cannot be sentimental about who they have working for them. They want results. They are willing to invest to get those results, and don't really care who the manager is so long as he's in their view the best man for the job. If they trust Kenny they will back him, if they don't they will dispose of him. This middle ground of we're not sure so we're going to keep you but not back you makes no sense.
If you ran a business or had a position of budgetary responsibility and you did not meet your targets I'm sure you'd have a sit down with the owner or boss sooner or later. He'd want to know why you did not meet your targets, and what are your plans are to do better going forward. If they accepted your reasons for the missed targets and felt you had a good plan going forward they’d back you. If they did not, they'd find someone better to replace you with. But why they'd keep someone they did not think had done a good job, are not sure can do a good job going forward, would be a recipe for disaster, even more so if they deliberately decided to cut your budget as well.
There is a saying here, and I'm sure it’s used over there. Don't throw good money after bad. If that is the case Kenny is gone. But then there is another saying, double down. If that is the case Kenny stays, and he gets what he asks for, or as close as FSG feels they can responsibly afford. Your suggestion implies throwing just a little good money after bad. Is that a new British expression I'm not aware of?