Ovinomancer
No flips for you!
Some spells are instantaneous but have lasting effects, like damage, being stunned, or your move speed being reduced by 10 feet for 1 round; those effects are not dispellable. The damage caused by those beams is not dispellable.
The ability to shoot beams on an ongoing basis is an ongoing magical effect. Call lightning has a duration of up to 10 minutes, during which you can call another bolt on your turn as an action. You can dispel call lightning while it is active. If eldritch blast really gave you the ability to shoot several beams over a certain duration, then the spell would have that duration.
]Call lightning is not an instantaneous spell which gives you an ongoing magical ability to call bolts of lightning for 10 minutes, and eldritch blast is not an instantaneous spell which gives you an ongoing magical ability to shoot beams for your entire action. The beams are the spell effect, and spell effects exist entirely within the duration.
Being coated with ice may slow your movement for a few seconds, and being stunned by an instantaneous slap might be the result of magic, but not magical in itself. But the ability to shoot beams of force is definitely magical; you can only do it because the magic exists, and when the magic stops existing then you have no magical ability to do so.
Look, I don't think I'm going to convince you. Convincing you was never actually my goal. My goal was to find a solution space that works for me, and see if it works for others as well. I have an explanation that is workable for me. I tried it out on you to see if it helped you. It didn't.
I have very little interest in opening up yet another unclear front (what constitutes legitimate 'results' of magic vs ongoing magic) in order to litigate the issue. I don't think you have any solid ground to stand on in your assertion that shooting a beam of force cannot ever be a result of magic gone, but must always be a result of ongoing magic, and I don't have any solid ground to assert otherwise. Opening such a nebulous space isn't going to provide any solid arguments for either of us, so I'm not going in.