Well the time to complete the investigation ranges from 5-75 days depending on the situation. See Tables 3-1 and 3-2 of AR 600-8-4 (Line of Duty Policy Procedures and Investigations).
AR 600-8-4 Extract
However paragraph 4-4 of AR 600-8-4 states:
4–4. Time limitations for processing line of duty actions Line of duty actions should be completed within the time limits given in tables 3–1 and 3–2. When an LD investigation, either formal or informal, is not completed within the given time, the reasons the report is late should be made part of the remarks section of DA Form 2173 for informal reports and as part of the investigating officer’s comments on DD Form 261 for formal reports. These comments can be expanded upon as necessary by the appointing authority, reviewing authority, or final approving authority. The mere failure to complete an action within the prescribed time or the failure to provide reasons the report is late is not a basis to disapprove, reverse, or change an otherwise proper determination.
There appears to be an exception based on this paragraph that allows the command to appoint the LOD officer and complete the investigation well after the 5-75 day requirements. I believe that the date for the LOD status would be the date that it became apparent that the injury was causing significant issues; since this was not immediately detectable at the time of your injury. That is just my opinion. Check with your chain of command and if they are not helpful; consider contacting the IG and/or JAG to ascertain a neutral opinion on the subject.