Mr Brickwood, 74, sustained 35 injuries during a violent attack at his home in Lindsey Avenue, Abington, Northampton, on September 26, 2015.
An unknown number of raiders had popped open a downstairs window before bursting into the pensioner's bedroom and delivering a brutal assault, an inquest into his death heard last year.
Mr Brickwood initially survived the attack and was able to call police for help, however, he died a short time later.
Detective Inspector Stuart Hitchon, from the East Midlands Special Operations Unit Major Crime Team, is leading the continuing investigation.
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He said: “This is very much a live investigation and three years on we remain as determined as ever to bring Mr Brickwood’s killer to justice.
“We still have information coming in and continue to follow up any new leads. We are also working with specialists at the National Crime Agency to ensure we make best use of the latest advancements in investigative techniques.
“New forensic techniques have been developed since the investigation began three years ago, as well as significant technological advances, giving us opportunities to further examine older evidence."
Seven people have been arrested during the course of the investigation, but no one has been charged in connection with Mr Brickwood’s death.
DI Hitchon added: “Our inquiries continue as we reach the third anniversary of Mr Brickwood’s murder, and I have no doubt that someone somewhere knows who is responsible for his death. I would appeal to them, or anyone who has anyone other information, to come forward and tell us what they know.
“I would also like to take this opportunity to thank the local community and David’s family for their ongoing support during this investigation. We have had a lot of useful information from many people and I thank them for their assistance.
“However, I want to appeal to those who still have information they haven’t yet shared with us, for whatever reason, and would urge them to get in touch. This is not going to go away, and we are not going to go away.
“We want to hear from anyone who has any information about David’s murder, no matter how insignificant they think that information may be – it may just be the piece information that provides the key to this investigation.”
Anyone with information about Mr Brickwood’s death is asked to contact Northamptonshire Police on 101. Alternatively, they can call independent charity Crimestoppers anonymously on 0800 555111.