I need arguments that support and refute the idea that Germany was without effective political leadership from mid-1944 to the end of the war.

I tend to agree with that thesis, and I think a better
series of arguments can be made to support it, but here are two arguments for each
side:

Without Effective
Leadership:

1)  Personal Health of
Hitler/Assassination Attempt - By the time of the Allied invasions on
D-Day, Hitler's mental health (or what was left of it) was shaky at best.  Demoralized
and depressed by battlefield defeats since Stalingrad a year earlier, he became
increasingly reactionary and irrational when issuing orders to his commanders, and
increasingly paranoid about those in his own government.  The assassination attempt on
July 20, 1944 was very nearly successful, and left Hitler partially deaf and with a
tremor.

2)  Isolation of the German
government/Allied bombing - As Allied bombing raids reduced every major
German city to rubble, communication, transportation and security became increasingly
difficult for Hitler and his general staff.  This eventually drove him into the bunker
below Berlin, where he was told what he wanted to hear rather than the stark reality
facing his country.  From there until the end of the war the German SS and Gestapo
effectively managed the country while the Wehrmacht fought the
war.

With Effective
Leadership:

1)  Hitler's subordinates managed
the country well in spite of Hitler - Those Nazis and commanders who
worked under Hitler were often in better mental and physical shape than their Fuhrer,
and were intensely motivated by the defense of the Fatherland, and so obeyed Hitler's
orders while tweaking them to make more practical and military
sense.

2)  Climate of Fear/Security Apparatus
- Most of Hitler's opponents and potential opponents had been arrested,
killed or sent to concentration camps by 1944, and the Gestapo secret police and the SS
ruled by fear with an iron fist.  The conspirators in the July 20th plot were hanged
with piano wire and it was broadcast over the radio.  No effective resistance to Hitler
took place after that, and while it was a losing cause, Hitler still managed to stay
alive and in charge to almost the very end.