Ok, long distance detective work time.
1) Can you define trigger locking up? IE trigger is rock solid and won't move, trigger grates and wiggles a bit but doesn't do anything, trigger flops around and nothing fires, trigger moves as it should but nothing happens, trigger is under tension from bolt but seems jammed etc? Does the action jam shut, or does it continue to work properly with the trigger jammed? Does the trigger work with the bolt out?
2) How fast are you shooting these 10 rounds?
3) Does this tenth round trigger lockup occur only when firing live ammo, or can you cause it to happen from dry firing as well (IE 10 or 50 times in a row)?
4) Is your bolt head/sleeve going fully into battery?
5) When you pull the trigger, does the bolt sleeve move forward at all, either dry firing or live firing?
5A) does this change over time? IE does it begin to move forward as the trigger is pulled after you've fired for a while?
6) Have you extensively cleaned the bolt, trigger group, and inside of the receiver with solvents or very hot soapy water until it comes out clean?
7) Is the safety engaging itself, or dirt in the safety engaging the bolt? Are there any shiny points of wear that're clearly occuring while you're firing?
My thoughts are:
1) The more info we have on the trigger's behavior the more we'll have an idea of what's going on. At this stage there's not enough info to know if the trigger is even the cause, or if it's the only problem. Info here will help.
2) If you're shooting very fast (10rds in 10 seconds or less), then it could be heat, but doesn't explain why this' happening. If you're shooting slowly, or are able to keep your hand against the receiver ring, there's not much chance it's heat expansion (but could be related to #5 and old oils gumming things up). Heat shouldn't directly affect the trigger group so far back without pretty extreme heat at the chamber (think wood on fire, rounds cooking off in the chamber) but may be causing the bolt head to not fully rotate, which in turn is not allowing the gun to fire properly - if it's jammed then the head wouldn't lock on the trigger pull, the bolt sleeve wouldn't travel forward and the trigger would appear to do nothing. See #1 for whether this could be a factor.
3) If the trigger jam occurs only with live ammo I'd think something's working its way free under recoil, or from the trigger moving. If it also occurs while dry firing at all, then similar issue but caused by the trigger moving rather than recoil. This will also help establish if heat is an issue.
4) If the bolt/head isn't going fully into battery, this could be a factor. Should be pretty evident, but might not be.
5) Related to #4
5A) If the bolt begins to stop earlier and earlier, especially when firing live ammo, then it could be tight tolerances and heat expansion, or dirt/grime/old grease liquifying and gluing to the bolt.
6) If the gun has not been heavily cleaned, due to the complexity of the action, these issues may just be caused by a chunk of hardened grease, or liquifying/solidifying grease on the bearing surfaces within the receiver ring. The tight tolerances of the Ross are more prone to seizing up from gummy environments than others. Locking surfaces can always be prone to this, especially when they're wide. Strong solvents or very hot soapy water work best for this, along with a good small stiff brush to really get inside parts. Culprits may include: The inside of the receiver ring locking surfaces and areas of bolt head travel; inside of bolt sleeve, outside of bolt head, inside of bolt head firing pin recess; inside of safety; all of the trigger group. Hot water and soap works great but beware of flash rust.
7) Bright spots may indicate a rub or wear point, or point of failure that is causing the issue. Once the gun is clean use a sharpie marker to cover them all and work the action a couple times while dry firing. Check to see if any appear. Do the same while live firing, then when the problem appears, check the rub marks again. I'm thinking of issues like a pin migrating under recoil, that weird football shaped retention ball in the bolt, the safety engaging the bolt, the trigger roller bearing seizing or jamming up etc.
Anyways, that's what I would check to begin with, before looking for more exotic issues. Anything that's worn, loose, wobbly, grates when moved or not consistent in its movement is suspect as far as defective parts. HD video of the whole action while shooting including the moment it jams would help.
