Should I keep talking to her ?

Hi

Here's the story,

I met her in person but rarely see her a lot but started talking to her on Skype a lot for a good 2-3 months. Our conversations are usually fast and neither one of us would delay on replying back to each other. She typically is always the one who starts the conversation every time which is odd. Day after day, I have started noticing that conversations become a bit boring and her replies are not instant than it was before. She takes quite a while to reply even which is a pet peeve. Then it got to the point where sometimes she doesn't even reply back!

When she does not reply back, we don't talk for about 3 days to 5 days even though she is online Skype. I know most of you people would say, "Well, why don't you start the conversation first". I did once where I started the conversation and she replied fast but then it turned out that I was the wrong person to receive the message. This means that she doesn't want to talk to me at all. Getting back in topic, I have noticed that in these 3-5 days, she talks to me like for one day around noon typically when she is at work and then 3-5 days later, we talk again. We talk for good couple of hours but then the conversation just dies and when she is back home, she doesn't bother to reply to my message that I sent her. She has messaged me before curious if i'm busy and then asks why I'm busy then apologizes to me for being so busy.

Not really a big deal but she does pop up in my notifications and I just talk to her but i'm always curious.. should I continue talking to her?