What makes learning more difficult as we age?
The answer(s) to this question can fill libraries. But I can give a few pointers here, as the question is relevant and timely, giving the tendency to an ever increasing life expectancy of the general populace in developed countries (notable exception: US). 

I think your question can broadly be answered by the fact that degenerative processes in the brain slowly, but steadily, impairs all of its functions. Possible reasons for the specific decreased capability of the brain to adapt itself to new situations are:


The hippocampus plays a critical role in forming memory representations that are important for flexible cognition and social behavior (Rubin et al., 2014). Decreasing hippocampal neurogenesis during aging may impair the functioning of the hippocampus (Couillard-Despres et al., 2011) 
Degenerative processes in the striatum impairs implicit learning that is necessary for mastering new tasks (Rieckmann &amp; Bäckman, 2009);
Deficits in serotonin and dopamine neuromodulation in various brain structures due to degenerative processes during aging results in decreased learning and decision making (Eppinger et al., 2013);  
Age-related altered neurosteroid levels may impair cognitive abilities (Vallée et al., 2011).


And the list goes on. 

References
- Couillard-Despres et al., Gerontol (2011); 57: 559–64
- Eppinger et al., Ann N Y Acad Sci (2011); 1235: 1–17
- Rieckmann &amp; Bäckman, Neuropsychol Rev (2009); 19(4): 490–503
- Rubin et al., Front Hum Neurosci (2014); 8: 742
- Vallée et al., Brain Res Rev (2001); 37(1–3): 301-312