There were two episodes of The Big Bang Theory in which Penny did not appear, these being season 4, episode 5, "The Desperation Emanation," and episode 6, "The Irish Pub Formulation." While Leonard and Sheldon never missed an outing, Penny had good reason for her two-episode absence. Cuoco fell off a horse while riding and broke her leg, leading her to miss two installments as her injury healed. An accomplished equestrian, Cuoco explained the accident in an appearance on The Ellen DeGeneres Show. Her leg was broken when her horse threw her and stood on her leg, leading to a lengthy recovery process.
Ever since The Big Bang Theory's pilot episode, the show relied on Cuoco's presence. While Leonard and Sheldon's dynamic was funny, the pair were friends for years before the series began. Similarly, Raj and Howard were longtime friends of the show's heroes, and thus, there was no serious conflict between them. However, Leonard's attraction to Penny was the spark that set the events of the series in motion. Needless to say, her absence from The Big Bang Theory season 4 was keenly felt. Even though Leonard and Penny were not dating during the episodes in question, the absence of the couple's chemistry was still hard to cover up.
To allow Cuoco to return to work while her injury healed, her character became a bartender instead of a waitress. This allowed the series to cover up her injury on-screen. The Big Bang Theory's goofy sitcom storylines meant that Penny's sudden career shift didn't raise any eyebrows. Meanwhile, Penny and Leonard's well-timed breakup made her absence less suspicious, as the couple was already avoiding interactions with each other in-universe. Thus, The Big Bang Theory was able to cover up Cuoco's injury until it healed completely, even if meant one of the sitcom's most-loved characters didn't appear in every episode.