The proportion answered in the target time fell from 77.9 percent in December 2015 to 47.3 percent in March 2016.
South East Coast Ambulance Service (SECAMB) said it took more than 100,000 calls in March and the service "continues to be extremely busy".
SECAMB said it "recognises the need for improvements".
The figures are in a report for West Kent Clinical Commissioning Group (CCG) which suggests "high call volumes, staffing issues" and GP out-of-hours "service failings" could be causes.
SECAMB said it was "working hard to recruit and retain more staff in order to improve performance".
It said last year 70% of calls were answered in 60 seconds and it had outperformed other regions on dealing with calls with a higher clinical risk.
Earlier this year, a report found "fundamental failings" at SECAMB over a scheme to delay response times for some NHS 111 calls.
Janice Kent of the Central Sussex Independent Patients Forum said it was "worrying as until a problem has been dealt with, you do not know how serious it is and if people are switching to 999 that will clog the system."
SECAMB took over the NHS 111 service for Surrey, Sussex and Kent in 2013 and uses call centres in Dorking and Ashford.
The NHS 111 helpline in Surrey, Sussex and Kent answered fewer than half of calls within a minute last month, according to provisional data.