Like many 'why did x disappear in the Early Medieval period' questions, the answer essentially boils down to logistics. One of the main benefits of the Roman Empire was the economy of scale that it could effect. The vast Imperial logistic networks allowed, for example, provinces of the Empire to specialise in agricultural cash crops in the knowledge that their staple food could be imported. Similarly, Rome was able to establish vast workshops to essentially mass produce armour. The stereotypical 'Gallic' Imperial helmet of Roman legionaries had several 'Italian' types which appear to have been mass produced: in a large workshop with such a modular design, it would have been easy for individuals to have specialised in making, say, left cheek guards, while another made neck guards and so forth until all the separate components could be assembled.

With the decline of the Roman Empire, blacksmithing, as with most things, falls back by necessity on local systems and networks. In agriculture, vast Imperial villa estates growing cash crops are abandoned, for example, replaced by a return to infield-outfield subsistence farming based around individual settlements or farmsteads. In a similar vein, mass workshops are no longer as viable, and instead blacksmiths are required to work on a local scale, producing not only weapons and armour, but also making and maintaining the agricultural tools vital to survival.

Weapons, and armour in particular, are extremely time consuming, and thus quite expensive. Most fighters in the ninth century fyrd, for example, would have counted themselves either extremely lucky or very wealthy to have a full shirt of mail. It is unlikely that everyone even had a helmet. Given the time and expense constraints, common helmet designs by necessity had to revert to fairly basic patterns that could be relatively easily and quickly assembled in small scale.

Of course, that isn't to say that all early medieval helmets were so basic. The famous Sutton Hoo Helmet is extremely intricate and cheek and facial guards are integral to its design. Of course, such a master work of metalwork would have been the preserve of royalty or at the least, the ranks of the nobility who could afford the craftsmanship and had the luxury of being able to wait for a helmet to be made.

I would suggest that there are three notable reasons that helmets with cheek protection declined in prevalence.

1 - Emphasis on cavalry. Warfare in this period placed increased emphasis on cavalry, and cavalry at most periods of history has emphasized situational awareness over protection in their helmets. Classical Greek cavalry, including the cavalry of Alexander the Great used the very open Boeotian helmet in preference to the many other types of Greek helmet with excellent face and cheek protection, and virtually all of the different helmets of Napoleonic era cuirassiers, who were under fewer resource constraints than was true in late antiquity, tended to keep the cheeks free of solid protection (although reinforced straps were typical for cuirassier helmets) in order to preserve the vision and hearing of the cavalryman.

2 - The advent of mail and scale coifs. The characteristic Norman helmet was often worn WITH a coif or extension of the mail shirt, but mail coifs of some sort seem to have become prevalent in the third and fourth centuries. You can find some evidence for this in the Battle of Ebenezer fresco in Dura, or from the illuminations of the fourth-century manuscript Vergilius Vaticanus. These coifs would have provided cheek protection. It isn't clear whether these were worn with helmets, but if they were not, then the helmet without cheek guards would then be an option specifically suited to the man who wanted to protect from a blow from above, but didn't want to have his side vision and hearing obscured, and if the helmets were worn WITH the coifs, then the helmet would then serve as reinforcement, rather than complete head protection.

3 - Increased use of more mobile shields. The classic Roman scutum or hopilite aspis shields were not very mobile, and were very focused on fighting in a line formation. Many of the shields in late antiquity through the early middle ages seem to have been adapted for use to block actively, so a competent fighter could reasonably expect to protect against a slash to the face as well as he could protect other parts of himself. Reenactment combat insights should be taken with a good bit of salt, but it is pretty clear that the use of one of the earlier line-combat focused heavy shields tends to lead to a LOT of blows across the face when fighting in line.