Well, the official continuity has already explained why this is. According to Lucasfilm, every R2 unit has a warranty of 20 years. After that they are not guaranteed to work perfectly. So, since over 20 years had passed by the time of the OT, he had expired. Another possible explanation is evidenced in the droids animated series. In that series, with each owner, R2 gets his parts and tools changed and customised. All it takes is for an owner to remove the rockets, which is likely what happened. That's the storyline reason why he didn't have them. In reality, however, it was obviously due to technology limitations and such. It's also just another example of Lucas' vision changing.

. Hope that answers your question.