The latest bank stress tests from the European Banking Authority (EBA) to some extent justify those concerns.
The tests show that, in general, the health of the banking system in the EU is improving.
The EBA stress test seeks to gauge bank balance sheets against two possible economic scenarios — a baseline and an adverse scenario.
In other words, it seeks to model how bank capital would be affected by different economic scenarios.
As such, it is a test of the resilience of the banks in the event of another economic shock.
The stress test looks at the weighted average common equity tier one (CET1) capital ratio, which is a measure of a bank’s capital relative to its risk-weighted assets.
Of the 51 banks in the test, the average outcome was 13.2%, which is 2% above the 2014 exercise and 4% above the 2011 exercise.
Even in the event of the adverse economic scenario, it is envisaged that in 2018 the banks tested on average would still have a stronger capital position than in 2011. This marks progress.
While the average health of the banks in the EU is deemed to be healthier, Ireland and Italy have been highlighted as cause for concern.
In the event of the adverse economic scenario, the CET1 in Ireland is projected to fall to 5.2% and in Italy to 6.5%. Both are around 12% at the moment.
Basically, Irish and Italian banks are still deemed to be in a vulnerable position in the event of an economic shock.
This suggests that banks in both countries will have to pay close attention to their balance sheets, with the implication that further capital may have to be raised (this is not an obligation at this juncture) or lending may have to be curtailed at some stage in the future if economic conditions were to deteriorate.
It has been argued this week by Irish stockbrokers amongst others that the adverse scenario is a bit harsh. The EBA models a decline of 1.7% in eurozone GDP between 2015 and 2018.
This compares with a decline of 1% between 2008 and 2011.
Despite these valid reservations, it is a cause for concern that AIB and Bank of Ireland are still not in a position of sufficient strength to withstand another significant economic shock.
Of course, such a shock might never happen. Famous last words.
Two significant economic data releases this week are indicative of a solid economic performance, but also demonstrate a note of caution.
In the first seven months of the year, an exchequer surplus of €862m was recorded, compared to a deficit of €647m in the first seven months of last year. This represents an improvement of €1.5bn on 2015. This improvement is due to total tax revenues coming in €2.1bn ahead of last year.
Total voted expenditure was €138m ahead of last year and non-tax revenue was €224m lower than last year.
Tax revenues in the first seven months were 8.5% ahead of last year and were €644m ahead of expectations.
Corporation tax receipts were €482m ahead of expectations. The Vat undershoot of €292m in the first seven months is not easily reconciled with the growth in retail sales in general and car sales in particular.
Of more concern is the Vat undershoot of €61m in July. Not surprisingly, consumer confidence took a bit of a hit in July, post the Brexit vote.
The latest labour market data show that the significant downward trend in Irish unemployment over the past couple of years has run out of steam in recent months.
The seasonally adjusted number of people unemployed has effectively remained unchanged over the past three months and the unemployment rate has been stuck at 7.8% of the labour force.
Granted, the number of people who are willing and able to work and who cannot find a job has fallen by 29,800 over the past year and is 158,200 lower than the peak level of unemployment in December 2011, when the unemployment rate stood at 15.1% of the labour force.
Despite this solid progress, it should be a source of concern that the labour market appears to be running out of steam.
Perhaps Brexit uncertainty is starting to be felt in Vat receipts and the labour market. Time will tell.