In all the Deep Space Nine battles none of the ships appear to have shields, when they are hit by weapons fire the shield bubble is not visible. Why don't they show the shields?
This is a question that's bothered me for nearly 20 years now. Good on you for asking. I see a lot of attempts to explain the 'no shields' phenomenon rationally, but honestly there isn't a 'rational' in-lore explanation for it. It comes down to ease of storytelling.
Throughout the rest of the Star Trek universe contemporary with DS9 (i.e. TNG and VOY), visible (on impact, anyway) shield bubbles are ubiquitous, and generally it takes more than a single photon or quantum torpedo to destroy any warship from a major faction (Klingon, Romulan, etc.) unless said ship's shields are down. Phasers definitely couldn't one-shot a Klingon Bird-of-Prey (though because of size/strength inconsistencies and variants it's hard to tell what's what with those...), let alone take down its shields with a single hit. However, Star Trek writers are notoriously bad at maintaining consistency in their lore, which many times results in story-driven combat mechanics doing whatever the plot demands, rather than the plot giving any consideration to previously established rules of the universe.
If the large fights in DS9's dominion war were true to the way STS combat had been portrayed elsewhere, it would have taken significantly longer, with ships having to dance around as they whittle down each other's shields. The main problem the staff ran into, I think, was likely the need to portray large-scale battles within the allotted screen time in a way that would convey the action and excitement of the moment. A decision was probably made that more explosions = more excitement = better ratings, so any rank-and-file enemy fodder ships and 'redshirt' ally vessels were shown, for the most part, without shields for convenience, while any ships with main characters aboard (or that were of particular plot importance for a given episode(s)) were promoted to 'hero' status with the normal shield bubble (a.k.a. plot armor).
This is all apart from the argument concerning whether the shields should be visible as a whole or in part, or what shape or form they take -- I believe that's an entirely different discussion from what's being asked, and as such have sought to address the original question concerning their presence (or lack thereof) in the major combat during DS9's dominion war era.
What makes you think all shields have to be visible to the naked eye? And that all ships must have shields? Especially the small ones probably don´t have one.
Edit: It did answer the question until it got edited...
So first of all small ships. Shield by any means are pretty energy intensive, lets say a shield needs the same energy as the weapon to deflect it.
Example: 2 small ships 1 with 0.5 shield 0.5 weapon 1 with 0.75 weapon 0.25 extra speed:
The faster ship is bound to win.
Comparison: 1 of the above against a bigger ship. The weapons both wont do a lot, but if the fast one has a chance, the shield wont help agasinst the strong weapons. The speed though helps to dodge shots or flee.
Another clear win for the shieldless ship.
Big Ships most likely do have shields but as stated above they can but not necessarily have to be visible, they could be magnetic fields for example.
When those films were made special effects were hard to get by so they might just have chosen not to make them visible to save the work.
Basically: as shield tech as explained in several places shield is actually not a bubble, but a layer close to the hull.
On the other hand the shield bubble is so often depicted in various movies/shows/etc that it is unclear exactly how do they work...
For sure DS9 for the most part explained away the lack of shields as "Dominion advantage". In case of battles though... this is plot requirement. It would be hard to show any battle in such short scenes they had the time for in sufficiently "carnage-y" terms. So they made them gone in bigger battles.
Also, for quite a long time DS9 itself had "barely working" defenses, including weakened shields. Unlike most starbases encountered throughout, DS9 is not... compact design, so it naturally requires way more emitters in total, which again makes them less effective. Which shows time and time again.
And for last - the whole bubble should not be visible, as it is created by multiple independent shield emitters, so it should show only parts hit.