It's reassuring to assume that a friendship will last forever; sadly, sometimes even the closest of friends drift apart. Sometimes this drift may result from a falling out or misunderstanding. In other instances, it's simply a case of one or both of the friends becoming overwhelmed with work and/or life events and no longer having enough time for a social life. A handwritten letter is a thoughtful way to show an old friend that you miss her, particularly if the letter spends more time inquiring about her than talking about yourself.
Write an introduction that not only warmly greets the old friend, but also acknowledges the time gap since your last communication. Include a brief but sincere apology for this lost time, as well as a succinct explanation for this lapse, if you judge it necessary and not uncomfortably personal.
Include a short section briefly covering important events that have happened to you since you last spoke to your old friend. Pick a few events that you feel are the most important, and which may interest her the most, if the time gap has been lengthy and much has changed for you.
Write a longer section asking the old friend about herself with questions that reflect a genuine interest. Ask her what major events have occurred in her life since you last communicated. Ask detailed questions that show you haven't forgotten about who she is, such as inquiring how her family members or significant other are doing (mention these people by name), whether she ever got that promotion, how her novel has been coming along, etc.
Finish your letter with another brief apology for the lapse in communication, and express your desire to remain in regular contact with your friend. If she lives close by, extend an invitation to get together and reminisce in person. If she lives far away, ask if it would be all right to call her at some point soon.