Hampshire Fire and Rescue has received more than 1,300 complaints about smoke alarms fitted during home safety visits.
The faulty alarms, designed to last for 10 years, are bleeping intermittently after about two years.
As the batteries are sealed, there is no easy way to disable the alarm.
The service has said it would prioritise refits for those who are "elderly, frail or disabled".
Joyce Bolton, 84, from Boldre in the New Forest had three of the alarms fitted by a fire crews.
Ms Bolton said: "One went off with an unholy noise and I could not reach it, I'm not allowed to stand on chairs."
The fire service replaced the alarm four days later. However because of the demand for replacing alarms, it was not able to swap her other two alarms which are likely to start beeping in the near future.
The Chinese-made alarms were bought as part of a national purchasing arrangement and have the British Standard Kite Mark.
Around 250,000 have been fitted in homes across Hampshire.
Tim Gates, from Hampshire Fire and Rescue Service, said: "A small proportion are malfunctioning - we certainly wouldn't be expecting this number to go wrong."
Although 462 visits to replace alarms have been carried out, Mr Gates admitted the service would be hard pressed to replace all the alarms, alongside carrying out its regular emergency work.
He said: "If people are able to do it themselves, replace the smoke detector. We have to focus our attention on the most vulnerable and those who genuinely can't do it themselves."
Mr Gates added that although the alarms were bleeping, they were still able to detect smoke.