Clematis sometimes flower on last years wood and need pruning after bloom, in Spring. Or some will bloom on growth that occurs that same year. You have to decide, and websites do tell the two groups and what common cultivars belong to which.
My experience is that Clematis do well for me if their roots are in the shade and head in the sun, but I can see how a potted plant on a balcony cannot be given these conditions.
Just googling in clematis pruning times might lead to info.

Tx. I will try and find pruning info for my cultivar, though my question was more about the fact that it's never really thrived and sustained a little damage, and so it's not just 'regular pruning' I'm asking about, but more corrective/reparative pruning...whether I can do so now...or if it's too close to the cold season?

I did read that their roots need protection from heat/sun and so I have a thick layer of white rocks on top of the soil for this very reason...

tx

You are unlikely to damage a clematis by pruning, even at inopportune times. There are 3 different pruning groups depending on how and what time of year the clematis blooms but all young clematis should get pruned the same regardless of pruning group. Generally the timing is the same as for roses - late winter or early spring when the forsythia is blooming - but you can also do it during winter when the vine is dormant. Young clematis should be cut back hard - to two sets of buds - for their first couple of seasons to help encourage a strong root system and mutiple stemming from the root crown. After that they can be pruned as recommended for that cultivar.

The feet in shade, head in sun concept is really a bit of a myth :-) It is not the sun/shade or warm versus cool issue at play here but soil moisture. Clematis need an evenly moist root run and that tends to happen more often in a cooler, shaded siting. But by no means is that essential - provided one is diligent in watering, growing clematis in containers in full sun is entirely possible.

FWIW, there is an entire forum devoted to clematis here on GW. Lots of rather active participants there who can answer any additional questions.

Thanks so much Gardengal. I can always depend on you for great input!! ;-)