「直る見込みは？」「システム開発チームのシュバイシェン博士が現在闘病中のため、もう暫くはかかるかと・・・」

「？」「、・・・」

'Any prospect of it being fixed?' 'Dr. Schweischen on the system development team is currently battling illness, so it'll probably be a while longer...'

Literal

''Fix [possessive-の] prospect [topic-は]?'' ''System development team [possessive-の] Schweischen-Dr. [subject-が] currently battling-illness-[because-ため], a-bit more while takes [quotative-と-(omitted)]''

Workplace/IT support exchange with a touch of gallows humor about being dependent on a single expert. 見込み ('prospect, outlook, estimate') is a common word for 'forecast of a future outcome'. 闘病 (とうびょう) literally 'fighting illness' is the formal word for 'being ill, battling a disease'. 暫く (しばらく) is a slightly formal 'for a while'. かと at the end is a truncated かと思います, a polite hedge.