I have Conjure Flame Atronach spell which sometimes I cannot cast -- when it works it is fine. All my stats are good, but when I choose to cast it, it doesn't always appear. Any ideas why ? . I don't have the same problem with Bound Sword ,for example. I am level 10 and Conjuration is 26.

Martin Septim, Martin Septic ? Kill ,em all

Same problem here, no idea how to fix it though.

Do you have magic absorption?

If the answer is yes, then that's it. Magic absorption bugs out and absorbs your own summon. There is a mod to fix it.

If the answer is no, you need to aim better. The crosshair turns red when the location you are aiming is too far.

I do not know if I have or not. Is it a spell or a potion that I might have taken ? Or something that the Bound Sword absorbs ?

Common sources of Magic Absorb: Atronach Guardian Stone and Perk in Alteration

you have to make sure the crosshair is pointed near you, if its red its not gonna work..so once its not red it will cast..you can take perks to allow you to conjure things further out which i take...like 2 or 3 times further out than default.

had the same problem I fixed it by casting the spell towards the ground not in the air, for me it now works every time.

Point down at the ground before you cast a summoning spell... the range on them is terrible until you get perks to extend the range.
-Loth