I understand. I have a 3 yr old and 4 yr old.
First thing to remember, until kids are 4 yrs old (or more) they cannot make the generalizations that we as adults do. Example, I know my stove is hot when it's on; therefore, I know not to put my hands on your stove (just in case it's hot!) So, you do have to tell her a million times to put the pens up, she knows what it means right now, but really doesn't make the generalization to every time.
Kids lie to please us. This is hard for me, if I know dd1 or dd2 did something, I'm likely to ask "did you do yada-yada?" They are most likely to say no, not because they are terrible, but because they want me to be happy. They don't understand rhetorical questions. They think, if mommy asks, she doesn't know!!! I try to use a statement, "I see the pens are still on the floor, you are supposed to put them up when you are done with them. Do you understand? Let's clean them up now." This is hard to do, but I'm getting better.
It's the same with any kind of general command. For my girls, who can do a great job of cleaning their room, I have to remind myself to be specific. Put the books on the shelf, where do we put the stuffed animals, etc... If I just say, go clean your room, they head in there, but lose track of the tasks.
At this age it is so hard to remember that they are still really such young creatures. They may converse with adult-like phrases and do have incredible understanding & are learning by leaps and bounds, but their brains are so busy that they do get distracted and forget things.
And the generalization about the TRUTH is pretty hard. I sometimes will try to get my girls to understand by saying something silly and asking if it's the truth (example, it's raining purple flowers.) But at this age they understand enough that they want mommy to be happy, but do have trouble with the 'adult' concept of truth.
Sorry to be so long. Your daughter is where she needs to be and you are obviously very involved and attached, so give both of you a little slack. Just try to be very specific, very black & white and don't expect her to remember tomorrow everything that you worked on today. (Guess, I need to be better at practicing what I preach too.)