Re: Pretty disappointed in myself, looking to fix that.
I'll weigh in with more support for patience. In a manner similar to a baby learning to walk, when you're new to Aikido, you're rather limited in how much you can do.
this is true in nearly any new activity - basics, basics, basics, and then in conjunction with your learning the basics, your body also becomes gradually more robust, and you can get more and more out of a workout.
When you have got to a stage where the sensei pairs you up, doesn't teach, but calls out "attack - technique," (e.g., Shomenuchi - Iriminage") and changes the attack and technique every 10 minutes through 80 minutes of a 90 minute session (after warm up), with you and your partner taking turns for four attacks, you'll find that by the end of that 80 minutes, you will be rather - um - tired. As you adapt to more and more of those sessions (if the dojo has them, and doesn't do 10 minutes teaching, 2 minutes practice as I've suffered through from time to time) you will find that you'll be able to go faster and more dynamically through the whole session. At first, you'll be vigorous for the first little while, then longer, then you'll get through the entire session without needing to rest. Then you'll be able to pick up the speed, and keep it for longer times.
In sports training it's called progressive loading.