Even if they appeal this, it’s likely they would lose. This is regarding governmental structure, not some political issue. I doubt even the liberals would agree that the president has the power to just decide that the senate is in recess.
Liberals feel that this president has the power to decide anything he wants.
Agreed. They'd "lose" 5 - 4. Which means they are one judge shy of not losing, given that there are 4 leftist rubber-stampers who cannot even recuse themselves when it's obvious they should recuse.
I believe it very likely that the Supreme Court will refuse to hear this case; that they will consider it an “argument between branches of the government” that they will not wish to get involved in any further than necessary.
I predict this will stand as is for now.