I do video calls with my 2.5 year old god daughter every week, as she live in another state and keeping a close relationship with her is important to me. She insisted on carrying the phone we use for chatting around with her, we had to find an app to keep her from accidentally closing the chat session so she could safely carry it.
We have many 'games' we play over the phone, I'll often have her do ring around the rosie or dance with me, and she likes to 'knock me down' by hitting the phone until I pretend to fall etc. However, she also has her own game of burying the phone underneath her toys or putting it inside a box so I can't see anything and then mostly ignoring me. She will occasionally come back to check on the phone, and I'll act excited to be 'rescued' from the darkness, but she will immediately bury me again, and she only does that every 10 minutes or so. I will try to keep talking to her and interacting with her despite my inability to see and muffled sound, but it's hard to know how much, if at all, she is listening or understanding me while I'm buried, and frankly there is only so much I can come up with to say to her like this. Yesterday it was extra blatant, after spending time in a toy box when she was moved to the kitchen she found a paper towel just to cover my phone with, and later plastic bags to put me in, it was as if she was actively trying to figure out a way to cover me up each time I was freed :)
It's not that she is simply bored of me. She gets excited about the calls, or even asks her mom to call me. If someone else tries to get the phone out from where it's buried she will get upset and tell them not to. Yesterday her mom said I was going to go if she kept ignoring me she pulled the phone out fast and pleaded with me to 'No go, No go!', so I know she still likes to chat with me even when she seems to be ignoring me, but I still don't like to be ignored.
Another limitation is that I'm often 'alone' with her when we do our video chats. her mother is usually taking care of her baby sister or trapped in the kitchen, and she will always carry me to another room away from her Mom. This is a problem because I don't have an adult to repeat what I say or ensure she hears what I say. In particular I've considered suggesting that I would hang up if she didn't want to keep playing, but I don't know if she will hear me and I don't want her to come back in 10 minutes to find the phone turned off and not be able to understand why I'm no longer there. There is also the problem that she will hide the phone well enough that I often have to speak up to help her mother find the phone when it's time for bed, so if I do hang up her mother may lose her phone.
I'm looking for two things. First, what can I do to keep her engaged even when buried, and what can I do to try to get her to play other games that allow me to actually interact with her. What is most important to me is that she enjoys our chats and remembers me as someone that cares about her, even if that means getting shut in the dark occasionally, but I feel like such long gaps without interacting is limiting my ability to engage her.