Reichsbahn operated reasonably well practically until the end of the war
Reasons for this are easy to understand - unlike oil, Germany had ample supply of coal (Ruhr and Saar region, Kattowitz-Katowice in Poland etc ...). Direct threat for railway system came only from various partisan groups and from air attacks.
Partisans were a significant threat for railway system in areas where they operated (Soviet Union, Yugoslavia etc ...) . However, damage they inflicted was limited (destroying railway tracks, occasionally blowing up railway bridges etc ...) . Germans repaired damage relatively quickly and punishment for local population was severe. Overall, partisan actions against railway system had most impact if they were done in concert with conventional military offensives. One example for this would be partisan attacks on railway before and during Operation Bagration. Of course, in areas far from front lines and without significant guerilla force railway transport was not endangered by them.
As for air attacks, they could be divided in two categories: strikes by fighter-bombers and attackers, and strikes by medium bombers.
Fighter-bombers and attackers (think P-47 and Il-2) did try to interdict trains coming or going from rail heads near frontline. This was not easy task, as German trains were regularly armed with railway FlaK, and more importantly tended to travel only during the night in areas with heavy enemy air activity. During the day they were dispersed in railway yards, or were hidden in railway tunnels. Railway yards were protected by their own AAA, and railway tunnels were almost indestructible in WW2 (they required precise hits with heavy unguided bombs from low altitude). Also, right until autumn of 1944 large part of territory under German occupation was simply out of range for fighter-bombers flying relatively low, both in East and West.
Medium bombers (think B-26) were used to attack important railway and marshaling yards, railway hubs and non-moving rolling stock in general. They did fly at altitudes where they could avoid lighter FlaK (20 mm and 37 mm to an extent) but not heavier 8.8 cm. Overall, their operations were somewhat successful, but Germans countered them by dispersing rolling stock and concentrating AAA. In general, freight railroad cars were difficult to destroy completely (they are essentially wooden boxes on steel wheels), while locomotives were usually hidden. Worth to mention that Germany actually increased production of locomotives during the war. Finally, medium bombers themselves had limited range and could not strike whole German held territory until late in the war.
As for your novel, bear in mind that last major transports for Auschwitz were Hungarian Jews and that ended on 9th or 10th July 1944. After that trains mostly carried goods in and out from nearby factories practically until January 1945 and Soviet offensive that liberated the area. SS personnel would not have much problem traveling using trains, especially during the night.