deleting small number of rows hangs in tsql database
Might be that cascading foreign key that table [Shift Offer] has pointing to table [Availability], slows down your delete operation

Try following:

1) create nonclustered index on column [Shift Offer][availability_id_fk]
and try running your query again; see if nonclustered index speeds things up

2) if still running too long, try disable the foreign key at all (run sql command)

alter table [Shift Offer] nocheck constraint [paste your constraint name     
here I guess its availability_id_fk]


run delete command, and if succeeds and works fast, you will have to manually delete records from [Shift Offer] table, if it had any rows with availability_id_fk values that were deleted from [Availability] table, and  then enable foreign key back