There are style PLENTY of books being published with lines like "Her eyes begged me to" or some variant on that. The problem really lies when it's part of a pattern of using clichés. If in your whole book, you have one reference to someone begging with their eyes -- it's not going to create a problem and most editors won't change it.
Really, humans experience so much through our eyes. It's the dominant sense for most of us so we really can over use visual stuff in general when we write. And then when all the references are to eyes acting independently...it just points up the overall use.
But don't panic and think you can never use something like "I tried not to look at his begging eyes" or "she froze, not speaking, but begging with her eyes." Of COURSE you can use something like that. It's not evil. But be sure it's the smoothest possible phrasing (any sentence with eyes doing something be sure you rewrite the sentence a good ten times to be sure you have the smoothest possible reference since many times the whole "eye" thing is also in clunky phrasing). And be certain it's incredibly rare in your book. A little eye goes a long way.
[Edited to add: You WILL find that some editors with smaller publishers and less overall experience in the industry will have "hair trigger" responses to a bunch of things. They'll insist you never use past perfect tense, for example, or you never have something like "she froze, not speaking, but begging with her eyes." It's because their inexperience leads to less nuanced editing. It results in a lot of "never do that" editing. That can be an issue, and one where ultimately you have to decide whether it's worth sticking with the smoother, better writing or rewriting to meet a "absolutely never do *blank*" mentality. It's YOUR book. Never forget that. That doesn't mean you should try to keep a gazillion multipart verbs or a cartload of references to eyes acting independently of the rest of the body -- but when you KNOW the phrase you wrote is EXACTLY the phrase you meant, be prepared to explain yourself and then stick with your guns.
Honestly, there are a LOT of things in writing that we don't mean literally. Metaphorical uses of all kinds. And other figures of speech. We can pick apart Shakespeare if we insist only things that can be taken literally are okay. The lesson to embrace is that eyes as an independent agency is overused and may have been way overused in your work because it happens to lots of us. And the overuse has worn down a lot of agents and editors. But don't throw the baby out with the bathwater (another cliché that shouldn't be taken seriously
) -- don't twitch every time you've written something that isn't sensible when taken literally. Symbolic writing. Metaphors. Figures of speech. These are good things. Don't let anyone make you afraid of them.]