Cisco Switching/Routing :: 3350 - Network Based Application Fails To Open During The Day

I work at a hospital and one of our department uses specialized software created by Varian Medical Systems.  It has been brought to my attention that one of those applications has trouble opening during the day.  I had the users demonstrate the issue and from what they explained to they are supposed to be able to open the application, log in, and be presented with a list of radiology images to choose from.  Unfortunately, during the day this fails often and they have to try 3 or 4 times before it actually works.  It behaves differently after 4 pm, and seems to work after the 1st or 2nd time at that time of the day.  According to what I've been told this has been an issue as long as they can remember.
 
Varian has told me that they have done a number of things on their side to rule out their software and they think it is a network issue.  We used Solar winds Engineer's Tool set (specifically the Network Performance Monitor) to monitor their switch and it is reporting no errors and the utilization graphs show that the ports involved have very little utilization.  The most heavily utilized port is hovering between 10 and 5 person (Fa0/40).  I've included a network diagram, but basically we have 1 10/100 Cisco 3350 switch (c3550-ipservices-mz.122-25.SEB4.bin), 4 clients, and 2 servers involved.  They all are connected to the same switch at A-Full/A-100mbps.  Although the Network Performance Monitor doesn't show any errors or over utilizaton of the ports in the the CLI I do see 35 output buffer failures and 35 under runs on the port connected to one of the servers (Fa0/40).  They were a little higher and I cleared them about two weeks ago and then rebooted the switch, because I found that it could alleviate these types of errors.
 
They say the software use ports 5000, 55000, 55010, and 55020.  We tried a packet capture, but I didn't have enough experience/knowledge to get anything useful out of it.  I also checked the event logs on the clients and servers and nothing there indicates a issue in the software.  They want us to replace the switch with a gigabit switch, but we have a REALLY limited budget and I would rather not if it isn't necessary. What I could try in order to rule out the network?