Mom's not eating much during the day while I'm at work, I think she is feeling depressed. What should I do?

Nothing did more for my own mom's state of mind (that is, including, her mood, level of awareness, and desire to interact and participate within her own daily life) than having the ability to be around people of her own age. I tried for the longest time to try to get mom interested in activities with me that either she and I used to enjoy at some point or that she had enjoyed on her own...such as playing gin or doing paint by numbers. No matter what I tried or suggested or did, she was just not interested. She hasn't had any formal diagnosis of dementia but she had been started to have trouble remaining oriented to place (she would think this house was not our house and we needed to go home). But as time went on, and she just stayed in her room watching home and garden and such, she grew more and more disoriented and less participatory.
This was after she had broken her left hip. Then she broke her right hip and the recovery after that necessitated her staying in a local NH for skilled nursing care so that she could have PT and OT and hopefully at least regain the ability to stand up if not walk. She didn't really want to go but I wasn't able to take care of her 1 week after surgery all by myself at home.
And over the 90 days she stayed there, even though she was homesick and tried many ways to coerce or trick me into taking her home, she was steadily more bright and clear in her interactions and her mood was good when she wasn't giving in to homesickness. And I realized that even though she didn't really get into the socialization as far as talking to other residents and 'making friends,' she was still somehow benefiting from being around others who were her own age and in similar situations. It wasn't that I wasn't providing opportunities to relieve her boredom, it was the simple fact that she is 87 and I am 44.
That can be the same dynamic with a paid caregiver, sitter, or companion, too. They might be as cheerful as Pollyanna and as helpful as Mary Poppins and whatever else makes the perfect senior companion...but if they are from another generation, they aren't going to do much to help the feelings of isolation that I believe contribute greatly to the idea that seniors are depressed. It is, yes, depression, but perhaps not the kind treatable with meds (and often those meds have detrimental side effects exacerbated in the elderly and infirm). It is situational...it is tied in with loneliness and the lack of having someone to identify with. We all need that, no matter our age. When we are 15, we don't want to hang out with 7 year old's or 21 year old's. It is the same when we are 75 (although the acceptable gap widens a bit by then). "~)
And meals are more appealing when there is someone to sit down and eat with for most of us...most of us have to eat just to get on with our work and chores, whatever...but when you are no longer busy like that, meals become uninteresting and the incentive to eat is not there.

I say all this because I think that if you were able to hook up with some kind of senior companion program, where other seniors come to the home to spend time with other seniors such as your mom, and/or meals on wheels (which was an excellent suggestion)....or even, if possible, a trip to the local senior center a few times a week to eat lunch and be around others...I think she might eat better and probably shake off her blues.
It gets lonely, I think, for them...and we don't realize because #1 we are so busy and #2 we haven't yet lost most or all of our friends/cronies/peers.

Anti-depressants can help, also social interaction--senior center? The catch-22 with depression is that the things that you need to treat it (sunshine, exercise, social interaction, brain-stirring activity, etc) require effort to obtain unless someone else dumps you into the situation where you get those things effortlessly.

cheryl166 has some very good suggestions for you.

Your profile indicates Mom has dementia. At some point it usually becomes necessary to have 24/7 care for those with dementia. I don't know if your mother is there yet, but her lack of self-care during your absence may be an indication she needs more supervision than you can provide while you work. Calling her to remind her where the lunch plate is or ordering meals on wheels for her may help for a while. Eventually having her in a day-care program or having a companion for her during your working hours may be the best approach.

Have you discussed the possibility of an anti-depressant with her doctor?

Does she have to find her own lunch from food in the kitchen? It may be too much for her to figure out. How about meals on wheels? Delivering a lunch and usually a dinner is very low cost. She may like the short interaction of the delivery person and sit down to eat when the meal comes. Plus there is something for her dinner which may save you some energy. Check the local Senior center, city or county government office to send you in the right direction.

Senior Center may have some other suggestions including Adult Day Care she could attend a couple days a week. Interactions may help her and you so you don't feel so alone.

You may have to fix a lunch plate then give her a call during lunch time and remind her it is time for lunch.

God Bless.