Intermittent problems can be very frustrating to solve. You need the system to hard-fail to more easily diagnose what is wrong with it. We need more info to provide any type of clear troubleshooting path. If it is a hardware failure, then the steps needed to solve it are completely different than software related solutions. *The G1313A is an older model so it may just be telling you that it requires professional service too.
The very first thing I would look at is the INSTRUMENT LOG files. View them to see if any useful information was stored by the system during the event. That info, if present, may help direct you where to look next.
Next, I would determine if the failure is due to a hardware issue (the sampler is stuck or failing to respond to each step). You can manually operate the sampler/injector through the menus to see if you can make it fail by repeatedly testing each step and/or observing operation.
Wait-time errors are linked to the loaded method. Review the method to see if someone has programmed a delay to occur (wait for temp, wait for pressure, timed wait in sequence is set). The system usually does what it is told and sometimes people forget they the programmed a wait.
Your method(s) may be corrupt.Try loading a NEW, not copied, method and run it via Sequence to see if the same failures occur? Identify the conditions which cause the problem and you will be closer to solving it.
Here are a few other things that could cause a "Wait-Time" or failure of the A/I to complete all steps:
Corruption of the software, specifically the ChemStation software (but the Windows system files may also be corrupted). This is a common problem over time as the hard disk fragments and files are corrupted. It can cause all kinds of intermittent problems in control and data acquisition. The most frequent causes of this corruption are: use of screen savers, auto updating features or similar utilities (which must never be used on a data acquisition system) or when the computer used is not maintained (regularly cleaned and optimized). Another cause is when the HPLC computer is used for purposes other than the HPLC system. Ex. If the computer is used for web browsing, running non-ChemStation programs or has been connected to a regular computer network (it should only be connected to a private instrument network, away from traffic). The solution is of course to completely wipe the hard disc clean and re-install everything. Sometime you can fix it by not removing the software and just running a system repair utility [https://hplctips.blogspot.com/2017/11/repair-missing-or-corrupted-windows.html]; running Disk Cleanup and Defragmenting the drive.
Another related cause of these types of intermittent problems may be from the network connection itself. Any interruption in the communication between the computer and the LAN card installed in the HPLC system may result in loss of control of the HPLC system. This by design results in the system hanging right where it left off, still running initial conditions, ready to go, but not aborting. The solution here is to find out if the network card in the computer or in the HPLC is defective.