Does it shift up into any higher gears,or not?...if it seems stuck in first gear and goes into a neutral when it goes to shift into second,and wont shify up into any higher gears ,or only does sometimes,one possibility is the govenor gear may have stripped or broke,its made of nylon or plastic..it's not that hard to inspect or fix it,provided the cover its under doesn't have a crossmember or exhaust pipe right in the way..
On most GM trannys its located near the tailshaft,it is driven by a gear on the rear output shaft--to inspect it you either pry the tin cover off. or unbolt it if it has bolts (I'm not real familiar with the 700R4's) and then the govenor can be slid out with your fingers ,and the gear should be straight,not all concaved or stripped or broken..if its junk,its a 5-10 dollar part at a dealer,thats easily installed by driving out a roll pin..kinda looks like a distributor drive gear,only plastic..
I assume you have a 700R4,or a 460LE tranny..they have a throttle valve cable on the 700R4 that needs to be adjusted right or it will slip,shift at the wrong speeds,not downshift,it also affects the firmness of the shifts too..the 460LE's were controlled by the computer I think,and have solenoids that do the shifting,if one fails,you'll "lose"that particular gear..I think that might set a code and the check engine light on too?...
Unfortunately these trannys were not GM's best,and usually when they start acting up its time for a rebuild..most common failure is they wont go into overdrive or they slip between 3rd gear and overdrive,that usually means a clutch drum is shot or clutches are burnt..hope its just your govenor gear or a solenoid ,they arent too bad to fix--you must drop the pan to change a shift solenoid,they go in the valve body..a rats nest of wiring goes to them,it beats me how electricity works when immersed in oil!..(or gas too,in the case of an electric fuel pump sumerged in the gas tank!