Paragon said this was the lowest proportion recorded by the long running research, which is conducted by Pegasus Insight.
The proportion of landlords reporting a profit from their lettings activity also increased by two percentage points during the quarter to 86%.
Separate analysis from Paragon found that average gross rental yields reached 7.02% during Q2.
The findings come as UK Finance figures show that buy to let mortgages with arrears of three months or more have fallen for nine consecutive quarters.
These cases represented 0.52% of outstanding buy to let mortgages at the end of Q2, down from 0.68% a year earlier.
Paragon's research also found landlords were more confident about the performance of their own lettings businesses and rental yields than wider factors such as the UK economy and future property values.
Lisa Steele, mortgage lending director at Paragon Bank, said: "We often hear about the pressures facing landlords, whether that's economic uncertainty, regulatory change or the wider costs associated with running and maintaining properties. What's sometimes overlooked is that the overwhelming majority of tenancies work well and continue to provide reliable income for landlords.
"Record-low arrears, strong levels of profitability and healthy rental yields are all signs of a sector that continues to demonstrate resilience despite a challenging backdrop."
She added: "It's understandable that landlords remain cautious about factors such as the wider economy and future market conditions. However, when they look at the performance of their own portfolios, the picture is generally much more positive.
"Most tenants continue to meet their rental commitments, most landlords report operating profitable businesses and those are the factors that have the greatest influence on day-to-day confidence."
