Maybe even some isolated resistance nests could held for as much as 3 months, not necessarily in Eastern Poland but also some resistance nest in Central Poland - namely Warsaw. Warsaw could held much longer than it did in reality. Until Warsaw surrendered on 27-28 September (ceasefire started on 27 in early afternoon; capitiulation was signed on 28), the Germans only managed to capture part of the most outer line of defences (the line consisting of old, Russian forts built in 19th century - most of them were not very suitable for defence in WW2 conditions) and part of the city's suburbs. Warsaw could resist for much longer, but that would mean enormous cost in human lifes - especially civilians. Warsaw surrendered by the end of September because further fight was considered pointless.
Real streetfighting in densely built environment didn't really start until capitulation - there were mainly just combats for Forts and in the suburbs.
I made a map showing the German assault on Warsaw (and defensive lines of the defenders) in last days of September:
When it comes to defended forts, basically until the capitulation of Warsaw Germans managed to capture only:
In operational area of German XI Corps (18, 19 Inf. divisions + 24 Inf. division in reserve + mass of non-divisional artillery and Pioniere):
- Fort II
- Fort II a
In operational area of XIII Corps (31, 10, 46 Inf. divisions + 3 Leichte division in reserve + mass of non-divisional artillery and Pioniere):
- Fort "Mokotów"
- Fort "Piłsudskiego" (= "Legionów" = "Tsche")
- Fort IX (= "Czerniaków" = "Dąbrowskiego")
Germans also captured Fort "Szczęśliwice" ("Tscha") - but without combats IIRC - Poles attempted to recapture it several times.
Also Fort "Bema" was fought over - Germans didn't manage to seize it until capitulation, despite numerous attempts.
Fort III "Blizne" was captured by Germans early during the battle of Warsaw - later Poles recaptured it on 23 September (they also attempted to recapture it on 18 and 19 September but those attempts failed). Later one Polish platoon with 1 HMG stationed there until at least 26 September.
In operational area of German I Corps Poles didn't defend the old Russian forts at all but organized defence immediately in urban area of Praga district.