High protein turnover rate and protease inhibitors?
Scientists are recently finding (or coming to accept the notion) that, at least in eukaryotes, mRNA expression is poorly correlated to protein expression. There are several factors influencing translation regulation, such as siRNA or microRNAs, sequestering mRNAs while they are transported to various cell compartments, and others.  Even after the protein is made, there can be factors interfering with your expression reporter.  And as you mention, it may be degraded faster than you expect.  Cells try to keep proteins at certain expression levels, so if IL-1b is promoting expression without inhibiting the degradation pathway, degradation might kick into overdrive to bring the levels back down to normal.

Trying some protease inhibitors is worth a shot, since it's pretty simple by itself.  It should also increase your protein expression regardless of whether protein degradation is your limiting factor. If this doesn't work, or if it's prohibitively expensive to be sacrificing mice while you're working out a protocol (and is usually is), then I would turn to cell cultures and try and discern where you're getting blocked.  That kind of information will generally make a decent PNAS paper by itself.