There's not a lot of hard and fast rules pertaining to Aides and/or Paraprofessionals serving our identified children with IEPs. You can't dictate who is used as long as the IEP team determines need and one is provided. This is part of the administrative convenience and primacy provided to schools. You, as a parent, don't have the power to hire or fire specific people or employees either, as this is also the responsibility of the District.
Now, with that being said, the standard of responsibleness and appropriateness is the ultimate guide and analysis in this process and the school district needs to take that serious when placing certain people with children. There are times when the complexity of need or physical requirements for the job are too much for some Aides/support staff. Also, though not a law or outlined rule in the IDEA, I don't believe it is appropriate to place a male Aide with a female student with communicative limitations and/or bathroom/privacy needs.
Every school posts available jobs and those jobs have outlined job duties, including lifting requirements and other descriptions. If a school district chooses to hire an individual that might be unable to run a distance or far, lift a person, or fluently speak the child's understood language then it's not this person's fault that was hired but the employer that hired them. This is where you must take your concerns and make sure you print out job descriptions when they are posted on the school job listings, as this would prove beneficial to you as you make your case that (though the Aide may be super sweet and awesome) they are unable to ensure your child's safety if they elope or run away due to the reality that this Aide may use a cane, for example.
The hard reality is that we don't have enough special education personnel.... from SPED teachers to related service personnel to Aide support in classrooms. They don't grow on trees or in the ground so we must, at least in the shortterm, get creative in working with the District in how to best use the staff that does exist. I don't recommend whining or complaining incessantly about a problem that you didn't create but neither did your child's teacher.... use your creativity and work the problem with your child's teacher to see if you can identify solutions that work (especially at this late stage of the school year).