As Company Commander, Frederick would be expected to spend most of his time with the Regiment. A fair bit of the work could, and often was, fobbed off on the subalterns, but not all of it. There are administrative functions (Pay, Returns, etc. which need signing) and training (Battalion and Brigade drills) which are a Captain's job. Recent reforms in the Army specifically targetted this, as well as other, abuses of the holding rank. Thus, Frederick could not avoid being away, unless he sold out.

He may, or may not, have corresponded regularly with Eleanor. (I think this would have required a level of focused self-discipline, which doesn't seem to be one of his greatest virtues.) The problem with writing is that I expect all letters crossed the General's desk first. He probably wouldn't open a letter addressed specifically to his daughter. However, he is of a nature to take a great deal of interest in whatever might be in the letter. I can see him quizzing her about what her brother had to say, and even inviting her to read it out aloud. Just how openly could they communicate under those conditions?

They might route letters secretly through a third party, but that doesn't seem to be in Eleanor's nature.