Achilles tendon injuries are some of the toughest to treat and most frustrating for the injured athlete. Achilles tendon problems are deceptive - due to the nature of the tissue, when it warms up it becomes more pliable and the pain felt when the tissue is "cold" disappears, so often the athlete thinks it is fine to keep training because the pain disappears when exercising, but only returns when they cool down or when they wake the following morning.
Most of the tendon problems we see are in the chronic stage and have crept up over time. Treatment is intense and recovery times are quiet extended, usually needing a long period of time coming back to a full training programme. It is well documented in both physio and soft tissue therapies (such as sports, myofasical or remedial massage) that a very slow reintroduction to full sports load is what is needed to ensure the achilles is able to cope with the extra load.
As research into our soft tissue deepens, we start getting a better understanding why the slog is a tough one with a chronic Achilles tendon injury. What happens in a chronic injury is that the repair rate of the collagen in the tendon can't keep up with the damage being done. The strength of the tendon comes from the type of collagen in the tendon and how the fibres are laid down. Essentially a little like laying down carbon to make up a bicycle or aeroplane wing - some carbon is better quality then others and the tensile strength comes from how you lay those fibres down.
The changes in the tissue in a chronic Achilles tendon injury show that there is a permanent change in the type of collagen the body lays down, essentially it is replacing strong type collagen with a weaker one and rather than reverting back to laying down the strong collagen, it's like a switch has been flicked and the new collagen is the weaker type. The structure of the tendon is also altered, so the continuum of strong tissue is disrupted.
This starts making sense when we see clients having done all the correct rehab work, once back to full training their tendons start complaining again. More research is needed in this area, however understanding the changes in the collagen backs up what we are seeing in clinic.
So in answer to the question: Can I keep training when my Achilles starts hurting? I would say the short answer is no.
We don't have enough data to support how far into an injury this permanent change takes place in the tissue, however it seems that beyond a certain point it looks like it would need much more serious intervention to restore the tendon to a workable component.
If you are interested in a more detailed explanation on the changes taking place, this article offers references to the relevant data: tendinosis
You would be better off in the long run finding out what is causing the irritation to the tendon and resolving it before continuing with your plan. This can be tough especially if you have a big event you have trained hard for and paid good money to attend.