The couple whisked Chace to Britain last month in a final attempt to save his life after doctors in New Zealand told them his acute myeloid leukaemia had relapsed in January and there was nothing more they could do.
That was following a stem cell transplant in July last year after Chace was diagnosed with the cancer just days before his second birthday last March.
Now the aim is to keep Chace alive long enough for him to undergo a second transplant of bone marrow which can't be done within a year of the last one because it would be too toxic for the little boy's body.
Chace's bone marrow is more than 90 per cent leukaemic and doctors will give his body up to 42 days following the infusion to get that down to 25 per cent.
Mr Topperwien said it was a tall order but one that doctors would not compromise on if Chace was to remain in the four-month trial.
He said Chace's roller-coaster health was challenging for everyone.
"It can change so much in 12 hours. It can go from really good to really bad to really good to really bad all in a day."
The couple have been appealing to the public to help pay for the medical trial, which could cost up to $440,000, and for more Maori and Pacific Island bone marrow donors to help find a match for Chace when the time is right.
Fundraising efforts and donations, including two of $25,000 each from wealthy expatriate businessmen Eric Watson and Owen Glenn, have boosted the family's account to $125,000.
Mr Topperwien said a neighbour of his father's in Whakatane had generously given $5000.
Other donations, from strangers including New Zealanders in London, continued to pour in, for which they were very grateful.
"We want to thank everyone for the positive thoughts and prayers that are coming over to us, and the New Zealand community over here in London."
HELP CHACE
* Donations can be made to the Chace Topperwien. Fundraising account: 12 3217 0163111 00 at ASB.
* Find out how to donate bone marrow at bonemarrow.org.nz
* For updates and fundraising details visit the Chace Topperwien Facebook page or a new website called savingchace.com, which has already raised $6000.