Nineteen technicians are hired by Hawke's Bay DHB and all mainly work out of Hawke's Bay Hospital in Hastings.
Coxon said the DHB had been dragging its heels for far too long in trying to finalise a deal.
"There is something seriously wrong with the DHB's processes," Coxon said.
"After several strikes, we finally reach agreement around the table and it is approved by [HBDHB chief executive] Kevin Snee.
"We are then repeatedly told we will have the new offer within days, but after a month it still has not materialised. This is simply not good enough."
Snee said in a statement the DHB was hopeful a resolution would be reached to prevent the strike.