The woman, who does not wish to be named, spoke out after learning the work at Glenfuir Court will drag on until the end of September, when it was supposed to have concluded by mid-August.
The improvements will ensure lifts stop at every floor, rather than just odds or evens.
Discussing the delay at the high-rise where her 83 and 84-year-old mum and dad live, she said: “My mum is disabled and struggles with stairs and her lift, the even lift, has been off now for approximately three months and was supposed to be back on mid-August.
“I have been in touch with their councillor and they are now saying that it is likely to be the end of September before they are finished.
“I just think that this is appalling. There are so many elderly people who are having to struggle up and down one flight of stairs so they can exit the building.
“Given many have been isolating, now when things are opening up a bit they struggle to get out.”
A Falkirk Council spokeswoman said: “Our lift improvement programme in the high flats got under way just over a year ago, with nine out of our 13 tower blocks complete, with little disruption to residents.
“Unfortunately, we have experienced a few technical issues at Glenfuir and Greenbank which has delayed progress by at least four weeks.
“We apologise to residents for this disruption and will keep them informed of progress.”
In 2018, the local authority’s housing department first outlined its plan to provide lifts which service every floor instead of just odd or even levels in the region’s high flats.
The council also moved to reassure residents that every step was being taken to address long-running lift issues which began in April of that year and saw some pensioners become stranded in Falkirk’s Parkfoot Court.
After investing £30 million on its high-rises in Falkirk and Camelon over the previous 15 years, Falkirk Council committed to spending a further £1.2m in 2019 transforming each of the buildings’ lifts systems.