Buick cutting out on uphill incline

I have a 91 Buick Park Ave with 60,000 miles. Lately I have found that it may cut out when assending a steep hill if the tank is less than 1/4 tank full. It happened today. I was in the Ozarks and climbing a steep hill on the highway. As it slowed down I kicked the pedal to get it to downshift and it cut out. When I let off the pedal, it continued to run and barely made it to the top. I tried a couple of more times and it seemed to occur when it downshifted going up a hill, especially if I pumped on the accelerator pedal. Are there separate injectors that come into play in that situation? Could they be clogged? When I got beyond the mountains and on level ground it ran ok. Any ideas will be appreciated.