What causes ballpoint pens to write intermittently?

I would guess it's in part because of the viscosity of the ink. That would explain why the effect is more seen when it's colder. I don't know how doable it is, but you could try filling an ink cartridge with ink used for fountain pens, which is typically less viscous. You might get blotches of ink, but my guess is you won't get dry strokes. So maybe ink manufacturers used easy-flowing ink in ballpoints at first, but then saw it flowed too easily, and made more viscous inks. But this is speculative.

Typical ballpoint pen ink uses benzyl alcohol BnOH as solvent, together with viscosity enhancers (such as fatty acids) which vary from one manufacturer to another. BTW, benzyl alcohol has anesthetic properties and will make your tongue numb if you get it in your mouth (yes, I was a kid once), but don't take this as a test advice.

Like any solvent, BnOH evaporates over time, leaving the ink more and more viscous until the symptoms you described appear. BnOH has moderate water solubility, that's why adding water helps the ink to regain some of viscosity. Another possible additive is mineral oil: it's also compatible with BnOH and has the advantage of staying there for much longer than water. Both water and oil (especially oil) will worsen the ink drying properties. Note that you'll want to keep your pen upright at all times if you add any solvent to it.

However, adding solvents will not keep your ballpoint pens working forever: given enough time various components of the ink will polymerize, making it a hard insoluble resin.