UPDATE: Still having issues with the employee. Unfortunately it does seem that email management is not her forte. She doesn't seem to read them in a timely fashion, and often fails to respond.
Our CEO sent her an email last week that required a response that same week (clearly stated in the email e.g. "Could you please reply to let me know by Thursday"), she then sent a follow-up on Thursday afternoon when she realised the employee had left for the day and still not responded. She still didn't get a response. From what I can see it looks as though the employee just doesn't bother reading all of her emails at all. We're actually not sure what she does with her time as upon exchanging notes it seems none of us are really getting our delivables out of her properly. It's weird. It's kind of disappointing more than anything. She is experienced and not a junior so not really any excuse for such poor time management. I know she has been confiding in another colleague so I asked her about it, apparently she has been complaining that she has too much work, isn't sure what she's supposed to be doing, not enough time etc. But even the colleague said "but to be honest, she doesn't really seem engaged and I really have no idea what she's spending her time doing". And she never asks me any questions or clarifies anything although I continually offer extra support/time etc. So seeing we've been through her job description in detail with her and set some clear guidelines I'm not really sure what else we can do.
Some aspects of office etiquette I take for granted, and one of those is that people will check their emails, read their emails, and reply to their emails! (Although I take it for granted, I also mention it in their orientation!) It's really hard because this employee is a lovely person, very experienced, and is going through a rough time personally right now so I would like to cut her some slack. But we're going to have to push her to lift her game, we're not a charity and this kind of thing is just ridiculous. Right now she's not adding any value to our company or really achieving anything, not a good start.
But hey, perhaps she's just having an off couple of weeks... her first few weeks weren't so bad, but then again her first few weeks we knew she was brand new so didn't have any expectations. Now we definitely expect her to be doing something!! So hopefully she lifts her game.