Texting

My boyfriend and I have been dating for a while so we don't text anymore. I've brought it up to him and he says he'll text me more but doesn't because he hates it and is busy. We are very lovey and coupley when together but I just feel so distant from him. I don't want to be annoying about the texting thing. Is it normal for boyfriends not to text you when they don't see you for a couple days? He sometimes won't even reply to my texts or snapchats