Why does the BAe 146 have higher maintenance costs than other comparable jet aircraft?
higher maintenance cost and higher cost of operations in compare to other jets due to its complexity.


That seems ironic considering what Wikipedia says

According to the BAe 146's chief designer, Bob Grigg, from the very start of the design process, making the aircraft as easy to maintain as possible and keeping operator's running costs as low as possible were considerably high priorities.
Velupillai 1981, pp. 1245-1246, 1253.



Why is it more complex than other jets?

Because it has four engines? I believe short-haul airliners of similar capacity mostly have only two.

Why are the maintenance and operating cost higher?

Wikipedia says of the original Lycoming engines used:

The ALF 502 has experienced multiple issues. Its internal electronics could overheat, triggering an automatic shutdown of an engine with no option of in-flight restart, and certain rare atmospheric conditions could cause a loss of engine thrust due to internal icing.[29] Additionally, the BAe 146 experienced aerotoxic syndrome due to leakage of tricresyl phosphate (TCP) into its bleed air; this has been blamed on problems with leaking engine seals. Exposure to these toxic fumes is a dangerous health risk


Note: the above is speculation, you'd have to ask an airline maintenance manager.
There are interesting maintenance anecdotes / whinges at pprune

High price of spare parts.
Accessibility of some components.
N1 harness that goes through engine fan strut.
Quick release fastners needed on engine core covers.
FADEC harness (RJ) can't be changed without dropping the donk.
Lower engine power cables that freeze full of moisture.
Corrosion issuse with the gear bay longeron strut.
The nose landing gear steering lube leaks out and the internals corrode
Air con pacs are unreliable.
Honeywell apu's are unreliable, Garrets better.
Fuel tanks need proper draining off every day to get rid of moisture.
Tri-wing fasteners often fail on removal.