First I'm not an European Kestrel expert and every bird has different tolerances, but generally, based on what I do know ...
Quick answer is: Without a partner, the female will not be able to feed five chicks and herself. Kestrels (both ours and theirs) are very fast growing and need alot of food. She might be able to keep herself, or herself and a couple of the chicks fed, but there is the problem of the first week to 10 days when the chicks can't thermoregulate - if she's out hunting the chicks may die of exposure, even in a nestbox.
Question - I haven't checked out the blog, but the "observers", are they watching day and night? Are they watching in person or via the cam? Are they able to tell the male from the female if he is coming back at dark to incubate? We have had males at the Radisson who did almost no incubating and were very elusive - I spent days watching (in person on rooftops) and never saw the males anywhere near the nest/nestboxes.
Long answer is: the male may still be around just very elusive in which case there is nothing to worry about. If he really is gone, the quick answer applies.
Does that help ...