When thinking of Dorset's rare butterflies the Duke of Burgundy fritillary or the silver-spotted skipper come to mind as they are both only found at one site in the county but they are quite visible and easily recorded. The brown hairstreak is also only known from one site in Dorset so that makes it equally as rare but as they spend much of their life in the leaf canopy of ash trees they are rarely seen and so easily forgotten. Although the males rarely descend to lower levels the female does as she lays her eggs on blackthorn shrubs and will also feed on the flowers of bramble and thistles but even so, they are not easy to find.
The observations we have in the Nature of Dorset database show the brown hairstreak emerging in week 28 in the middle of July and then there are reports nearly every week until week 35 in late August. The text books say that they fly until the end of September but that does not seem to be reflected here in Dorset as far as the data we have from your tweets for 2017 and 2018. May be further north they emerge later and end later?
The only known site in Dorset would seem to be the Dorset Branch of Butterfly Conservation's wonderful reserve at Alner's Gorse where considerable work is done to ensure the population there thrives.