She had to do the returns not only for her and her husband's business, but others in the family too.
"I'd been away and was doing it on the day it was due and couldn't get on the internet. So I couldn't lodge my return and also I couldn't pay it. I was penalised 200 and something dollars, $190 for our own business."
• Read more: Premium Seniors grapple with chequeless future
Davie-Martin said the fine was eventually waived but the experience was "a pain".
"Every time I got on it, [the internet] would drop out before I could manage to do the entire return, and then I had to start from scratch and then I couldn't get on at all."
All main banks ending cheque use
Banks are moving to phase out cheques nationwide. Kiwibank stopped using them in February last year and BNZ, ANZ, ASB and Westpac are curtailing their use in a few months.
Davie-Martin is also a Rural Women New Zealand board member.
A recent survey by Rural Women NZ found 60 percent of respondents were worried about banks removing chequebooks.
Thirty-two percent of respondents use cheques to pay tax and 80 percent paid their monthly bills with cheques.
Davie-Martin is leading the charge against their phasing out, demanding action from government and banks.
"Firstly, I would like to see connectivity to every rural area prior to them completely phasing out cheques."
The government's rural broadband scheme is expected to reach 99.8 percent of the population, but this is not due to be finished until 2023.
Rural Women NZ said this overwhelmingly shows rural residents need cheques to run their day-to-day lives.
Also on average, the driving time to the nearest banking branch was two hours.
The organisation is writing letters to banking chief executives, asking them to keep cheques until every rural household has access to reliable internet and consistent cellphone coverage.
Small group of farmers affected
Federated Farmers president Andrew Hoggard acknowledged it was a problem for a small group of people, but admitted he had not written a cheque in about 10 years.
He said most farmers already have serviceable internet access.
"There is a big challenge for a very small group of people out there, actually [if] we put the effort into making sure people are connected then I don't think anyone's too sad to see cheques go."
Hoggard said the Tararua district in the lower east North Island and central North Island probably had the worst internet coverage in the country because of the land.
"You've just got to look at a topographical map to see what the challenge is, you've got lots of hills, lots of valleys."