good point: since the burn didn’t happen until her death one wonders what went wrong with the investigation on a missing ship whose distress signal somehow was that powerful.
Indeed.
By the mid 24th century, a subspace communication from Andromeda galaxy (2.7 million Ly's away) would have taken about 50 years to reach Starfleet (if 'Where no one has gone before' episode of TNG is any indication).... that's about 54 000 times speed of light (and Warp 9.9 = 21 473 times speed of light by 2371)... which means that subspace comms were traveling at about Warp factor of 9.915 (if you factor in the premise that past every increment after 9.9, speed increases exponentially) - without aid of subspace amplifiers.
Even with taking newest measurements of Milky Way into consideration that puts it at 150 000 - 200 000 lightyears large (not 100 000), it would have taken about 3 or 4 years for the signal to be heard throughout the entire Milky Way galaxy (if it was sent using 24th century level of subspace communication technology, which we know it wasn't - it was sent using FAR more advanced technology).
For the 31st century level of subspace technology... the signal would likely spread through the galaxy in seconds or less... heck, the hyper-subspace signals in 2377 allowed real-time communications through 16 000 Ly's of space - so someone SHOULD have picked up the distress signal well before the Burn happened.
But you do raise a good point as to what might have went wrong.
We do know that for the UFP, the Temporal Wars ended sometime in the mid 31st century... this would need to have occurred before the year 3064 (if we Burn happened exactly 125 years before the year 3189).
Daniels told Archer he was from 900 years in the past... so, from around 3051... and in 2153, we learn that Daniels told Archer the Temporal Wars came to a close. Now, those wars (to uphold the Temporal Accords) could have easily lasted some 50 to 60 years before they finally stopped... so, that would give the Federation (and the Galaxy) about a decade or less to recover (but the nature of time travel is such that any changes to the timeline were basically undone - so, no real casualties because it would be like a massive reset button).
The Kelpien ship probably left in 3063, or sometime in 3064... and the Federation knew where they went.
So, the ship crash-lands, and no one notices it went missing in the Verubin nebula (the very same place they were sent to investigate this 'Dilihtium nursery')?
Heck, Starfleet is METICULOUS with reports, so if the ship hadn't tried getting back in touch, SF would have had to send a ship to investigate (this would be even more pressing due to Dilithium shortages).
If a whole search party was sent after Voyager which lasted a good time (years) before it was finally/officially declared lost, what the heck prevented SF from sending 2 ships to go after the Kelpiens?
Something tells me the writers hadn't really thought any of this through carefully... or the Dilitihum shortage has gotten so bad to the point where it may have prevented any rescue operations... but, we see Starfleet and what's left of the Federation merrily putting out fires on a daily basis and sending fleets around... so something is not adding up.
Unless crucial technology was damaged on the Kelpien ship which prevented hypersubspace or even normal subspace transmission... which seems unlikely because in that case, the signal wouldn't be able to propagate through the galaxy to be heard in the distorted manner... or the nebula interfered with subspace communications to such a degree where it slowed them down (but given the nature of the Burn, you'd think the opposite would occur).
