Roman's strategy of staying back a bit obviously wasn't working because it left Penny with room to straight up ignore him. After a few weeks of hit-and-miss responses from her to his friendly, harmless texts about movies they had talked about before he received the first error message. It took a few more tries to realize that she had blocked his number.
Why? Was he really that annoying? He didn't even text her every day and she didn't seem like the type of person to ghost someone without explanation.
That might have been enough to deter someone else but he was more curious why she did that than he was offended by her actions. When Harry told him that Jacob and Missy were hosting a barbecue, his first thought was that Penny might be there. He wasn't about to miss the opportunity to potentially find out why she blocked him.
