The GMB union has warned that "someone could die" as kidney patients were missing vital dialysis appointments.
It said a new phone-app despatch system left some ambulance staff "sat around" and sent others to areas without phone coverage.
New contractor Coperforma said it was using "all resources at its disposal" to overcome "shortfalls".
Complaints of missed appointments emerged four days after it took over patient transport services in Sussex on 1 April.
Coperforma admitted it was "still not operating optimally" and said pressure would ease as more staff were registered on its system.
Paul Webb from Bexhill told the BBC he had to call 999 for his father Eric, who needs kidney dialysis, when hospital transport failed to arrive.
Mr Webb said: "It's horrendous, people are missing appointments and waiting for hours. Not everyone has got someone chasing bookings for them."
Gary Palmer of the GMB union said it was "dangerous" for patients to miss renal appointments, as "deadly toxics build up in the body".
He said his members were "struggling" with the new dispatch system knowing "regular patients will be sat at home or in hospital waiting for them to arrive".
Coperforma said more than 700 "call booking journeys" were completed in its system on Thursday, and by mid-afternoon it "logged 50 crews using the mobile app".
The GMB union has called a strike ballot because a sub-contractor Thames Ambulance is using single base at Sheffield Park and many staff travel further for work.
A union has warned that ongoing hospital transport delays in Sussex are putting patients' lives at risk.