Non-classical logics usually don't have a problem with the
deduction theorem, as long as they have no relevancy based
implication, i.e. if they are based on a residuate lattices.

Many people on the other hand believe that the deduction theorem 
does not hold in modal logics, especially not in interesting logics 
such as temporal logic. A typical argument goes as follows. 
In modal logic we would have an inference rule:

      P
    ----
    [] P

And therefore if a deduction theorem would be available, we
could proof P -> [] P, which is not desired. This argument
is for example informally repeated in Temporal Logic, 
[The Lesser of Three Evils][1], Leslie Lamport, Microsoft Research,
MSR-TR-2004-104.

Fortunately matters are not that worse. A more detailed
analysis is given by [Does the deduction theorem fail for 
modal logic?][2] Raul Hakli, Sara Negri, November 10, 2010.
In a Hilbert Style calculus HK the above rule should be
more precisely formulate as follows:

        |- A
     ---------
     G |- [] A

The deduction theorem then holds. Since we cannot prove
|- P in the first place, and therefore also not go to
|- P -> [] P. Besides a Hilbert Style calculus, the paper
also presents an equivalent Gentzen Style calculus which 
has the deduction theorem as an inference rule.

Bye

  [1]: http://research.microsoft.com/en-us/events/lucacardellifest/
  [2]: http://www.helsinki.fi/~negri/selected_pub/dedthm.pdf