Easy - holiday resort traffic was mainly concentrated into 6 weeks of the year. This would make very little impact on overall profitability unless the line could be mothballed for the rest of the year.
An interesting point which only regurgitates the thinking of the Sixties. It does not, however, address the needs of the resident populations of 'resorts'. The seaside branches in the West country are now thriving because the services are, largely, designed to suit those who live there.
To come nearer home, for me that is, the short branch from Barry to Barry Island was regarded as 'seasonal' until the late Eighties and had only a skeletal service during the winter months. The considerable resident population was ignored until someone woke up to the fact that it was there. Trains needed to travel half way along the branch to reverse and then stand idle waiting time at Barry. Madness, but on paper no doubt an economy. The sensible decision was made to extend the trains the extra hundred yards or so to Barry Island instead. It now has a year round frequency of 3tph.
As for mothballing lines, I know of one that never made it back to life. That was the branch to Porthcawl, a popular seaside destination. Consent was given to the withdrawal of regular passenger services on the 'assurance' that the summer trains would run. Porthcawl station remained open for enquiries and the handing in and collection of parcels etc. During the first winter of closure, my late neighbour, who was Station Master, was confronted by a gang of men who had arrived to demolish his station. Despite his protestations and frantic 'phone calls, the place was knocked down about his ears and the track ripped up. So much for 'mothballing'.
The annoying part of all this is that the branch served a population of around 25,000, taking Porthcawl and its outlying large villages of Kenfig Hill; Nottage and Pyle into account. It is now, probably, a lot more and all this in prime commuter country.
But there you are, it was a '
seaside branch'. Things are not always as simple as they look and had the line been allowed to survive, I'm certain, it would now be a thriving concern.
I'm sure that there are many other examples, known to people on this forum, which would have flourished, given the chance.