I want to make sure I understand correctly: Images are both displaying on screen and in print with an sRGB profile?
Test chart printing utilities should send image data directly to the printer without any intervening color conversions. You still need to make sure that the printer driver is not performing color conversions. Dive into the settings and verify that no color management is being performed. A quick check here is to make copies of the image with the sRGB profile assigned to one and ProPhoto to the other (crucial that the profile is assigned rather than converting to the profile!). If they print identically, color management in the driver should be off.
Windows does at times like to reset display profiles to default values. These can either be manufacturer supplied profiles or, if none were present in the display driver, sRGB. Your display calibration software can encourage the bad behavior. X-Rite's i1Profiler, for example, stores profiles as per-user settings rather than system defaults. I find more consistent behavior by storing Windows display profiles as system defaults. In the Color Management settings dialog, see if the "Use my settings for this device" box is ticked for your monitor(s). If so, uncheck the box and click the "Change system defaults" button on the Advanced tab. Choose the appropriate profile, tick "Use Windows display calibration" on the Advanced tab, and click Close more times than should be necessary to save the configuration.
Windows nonetheless still manages to lose calibration annoyingly often. We run a Powershell script triggered at both user logon and workstation unlock to reload the current calibrations.