Other RPs I've run or Co-GMed, there's a minimum amount of posts per period of time. Case in point, the D&D RP I'm in demands that I post once every four days, with a secondary rule stating that I must wait for two other posts before posting again. 

Now, in order to make that happen during slow periods, it is encouraged that we post about character thoughts, feelings, or small actions in their down time. I had one post where my character farted in a bathtub. It was regarded by many as art (sadly), but it kept interest up in a slow period, even kickstarting others' posts. There's always something to write about, even if you're just waiting out front. 

Describe a scarab beetle crawling by. Does it make little swishy tracks in the sand? Quiet scraping sounds against a stone? Is it carrying anything? Trying to hide from the broiling sun? Are you going to step on it? Maybe you're picking your nails with a knife, and/or tapping your foot impatiently. Perhaps you, too, need to let an unstable trouser-growl fly. 

Speaking of which: http://www.roleplayerguild.com/posts/3214659 Enjoy. 

Yes, I believe that the RP needs to progress. In the meantime, a little "getting to know you" or "flavor text" posting isn't going to hurt matters any. May even let our benevolent GM understand that we're still in play, active, and ready to move. Doing nothing says the opposite of this.