Sauron's trips to Sammath Naur

[Gordis]

Sam and Frodo saw Sauron’s road from Barad-dûr to Sammath Naur

Out from the Dark Tower’s huge western gate it came over a deep abyss by a vast bridge of iron, and then passing into the plain it ran for a league between two smoking chasms, and so reached a long sloping causeway that led up on to the Mountain’s eastern side. Thence, turning and encircling all its wide girth from south to north, it climbed at last, high in the upper cone, but still far from the reeking summit, to a dark entrance that gazed back east straight to the Window of the Eye in Sauron’s shadow-mantled fortress. Often blocked or destroyed by the tumults of the Mountain’s furnaces, always that road was repaired and cleaned again by the labours of countless orcs.

It seems that Sauron used this road regularly, so he had some business at Sammath Naur. What was he doing there? Was he obliged to go there in person to cause darkness that covered the lands to the West? Was he obliged to go there to make this strong eruption on March 9, the signal for the war, which had been answered by blue lightnings from the Morgul Tower?

If it was the case, then Shagrat's words: "The Eye is busy elsewhere" may have simply meant that Sauron (referred to as "the Eye" by the Orcs) was away from Barad Dur.

So let us see. There is about 50 miles between Barad-Dur and Orodruin: at least half a day hard riding. I don't think Sauron used a Fell Beast, because why then did he need a road maintained in order?

So, Darkness started to pour out of Mordor on March 9. Sauron was probably at Sammath Naur, and also made a signal for Morgul host to leave (It seems he loved dramatic effects: why couldn't he simply set the hour in advance or sent a nazgul?).
Sauron must have stayed there for several days: till March 13. Proof? The nazgul normally were able to send instant messages to Sauron. But they were unable to do so for a good while, most likely due to Sauron's absence.

`No, I don't know,' said Gorbag's voice. `The messages go through quicker than anything could fly, as a rule. But I don't enquire how it's done. Safest not to. ...'

'Bad business,' said Gorbag. `See here – our Silent Watchers were uneasy more than two days ago, that I know. But my patrol wasn't ordered out for another day, nor any message sent to Lugbúrz either: owing to the Great Signal going up, and the High Nazgûl going off to the war, and all that. And then they couldn't get Lugbúrz to pay attention for a good while, I'm told.'
`The Eye was busy elsewhere, I suppose,' said Shagrat. `Big things going on away west, they say.'

So, likely Sauron was away from Barad Dur and from his Palantir on March 9-13, thus overlooking Frodo's passage of the Crossroads (March 9), the Muster of Rohan (10), the Ride of the Rohirrim before they entered the Druedain forest (13), Aragorn's ride from Erech with the Army of the Dead (9-13) and the capture of the Fleet at Pelargir (13).

Likely, when he returned to Barad-Dur, he rushed to his Palantir and kept all his attention on Minas Tirith and Denethor and on the Pelennor, disregarding small matters, like a capture of a spy at Ungol. But his being away from Mt. Doom proved perilous, as his Darkness failed on the morning of the Pelennor Battle (March 15). I think, poor Sau hurried immediately to Orodruin again, to make new portion of smoke, and thus missed the approach of Aragorn up Anduin.

Sauron simply had too much on his hands, poor megalomaniac, never trusting his underlings enough...