I think this could probably be asked in the general matchup thread. Regardless, I'll let you know what I think.
I'm not an expert by any means, but playing as R.O.B. whenever the mood strikes me, I have a hell of a time against rushdown fighters like Sheik and Zero Suit Samus.
R.O.B. is a big, slow, floaty, unwieldy target and if you can get into his personal space, he's in trouble. Sheik and Zammy also have projectiles, and although Rotor Arm can reflect them in theory, it's difficult to do in practice: Sheik's needles come out too fast to warrant reflecting, and Zammy's Paralyser is slow but can stun if it hits. Sheik's needles are good for pressuring R.O.B. by striking from afar and piercing his defenses by taking advantage of his slow, cumbersome reactions, and if you pressure him into doing Arm Rotor to reflect them, you basically have a few frames to hit him with a n-air or f-air. Likewise, Zammy can stun R.O.B. and have her way with him as she pleases, and R.O.B.'s large hitbox makes him especially vulnerable to the grab -> pummel -> d-throw -> up-b kill combo.
Captain Falcon is a bit trickier in my experience. He has no ranged moves and has to get in close and personal for the kill. R.O.B. will take advantage of this by pressuring you with lasers and gyros, and a good player will be able to read your moves and punish you for them. Approaching from the air can work in principle, though R.O.B.'s u-tilt and u-air will still batter you if you aren't careful. His throws are also dangerous, as d-throw can lead to a nasty u-air combo that can kill at mid-high percentages and his u-throw is one of the strongest in the game.
R.O.B., at his core, is a zoner. He wants to keep you at bay. Rushing in for the kill and trying to beat him up by outspeeding him will only get you so far. R.O.B. relies on reads and punishes and will ensure you can't get anyway near to him. He can soften you up with these zoner moves and then finish you off with a u-smash, f-smash, u-throw or u-air. While he's also slow to run, R.O.B. can pressure you if you give chase by releasing a b-air, a powerful kill move that can be used effectively for chase punishing. If you're recovering as Cap, be wary of R.O.B.'s d-air, which is incredibly slow, but a guaranteed spike if it connects. A savvy R.O.B. will also make maximum of their gyros, pressuring you from afar by launching them as you rush in and dropping them on the stage to deny approaches. He can also play mindgames with them, charging and canceling constantly until you're not expecting it, and then release it to punish you for a whiffed move. Arm Rotor isn't very effective against Cap, as it's slow and has a lot of commitment to it, but if he uses it to pressure you, he can smack you across the stage and send you away from him. He can follow up with an upward laser or even more gyro pressure, so be wary of that. You're seldom more vulnerable than when you're either far away from R.O.B. (he'll zone you 'til you get aggressive and make a stupid mistake) or at mid-range from him (he'll punish you with a smash or grab if you're just close enough to get hit without hitting him).
For detailed insights on the Cap / R.O.B. matchup, either ask the Cap board or troll through the R.O.B. board 'til you find what you're looking for. Add my NNID if you want, we can have matchups and I'll show you what I know and how to improve.
Nice avatar, by the way. I chuckled profusely. ;3
