Ok, this is something I have been battling with for some time now. Recently the problem has gotten rather bad.
I have an 01 Honda Civic EX automatic that I have been babying to get it to run somewhat smoothly, but with the seasonal temperature change it has gotten worse. The car does not want to shift from 1st to 2nd and will only do it once I reach 20mph, this was normal for about 6 months. Now the car will not shift when trying to move from a stop. My thinking is that it has not downshifted into first. I had the transmission rebuilt 2 years ago. There is a slow transmission leak but I have kept it topped off. Sometimes it will not shift from 3rd to 4th… this is new.
My thought is that the shift solenoids are worn out and need replacing.
I do have random misfires, but I think that is a separate issue.
Also, it has almost no problem when driving from a cold start. It gets worse the more you drive or after the engine has reached running temp.