Do Jabiru aircraft have a long history of engine failures or other technical issues?
I don't know about a "long history", but the Australian aviation authorities (Jabiru is an Australian company) did introduce operating restrictions because of what they considered to be a high rate of engine failures. Note that Jabiru makes their own engines, unlike most other aircraft manufacturers, and as well as using them in their own aircraft they sell them for use in LSAs.

CASA mentioned 45 incidents in one year:


  These precautionary limitations follow a high number of Jabiru engine
  failures and power loss incidents, some of which resulted in aircraft
  forced landings.
  
  More than 45 Jabiru engine failures or in-flight engine incidents have
  been reported in 2014, with CASA recently becoming aware of incidents
  in previous years.
  
  Problems with Jabiru engines include failures of through bolts,
  flywheel bolts and valve train assemblies, as well as cylinder
  cracking.
  
  The failures affect a range of Jabiru engine models and have occurred
  in aircraft used in different flying activities, although many have
  been reported in aircraft used for flying training.


By itself, the number 45 doesn't mean much without considering more information about the number of aircraft, the number of hours flown, maintenance performed etc. and Wikipedia says that Jabiru didn't agree with CASA's decision (which isn't surprising). But presumably CASA did think about those things and still decided that there should be restrictions in place.