Can nosebleeds cause death?
Yes, it can, but it is extremely rare.


  ... nosebleeds are rarely fatal, accounting for only 4 of the 2.4 million deaths in the U.S. in 1999 [1].


The main issue is that epistaxis can be a sign of potentially fatal diseases:


  The instances in which nosebleed is potentially fatal are those in which there is a history of recent head injury, severe arteriosclerotic cardiovascular disease or an underlying vascular tumor in the nasal chambers. Fatal nasal bleeding has not been reported in children [2].


Here are some causes which can lead to fatal complications if left untreated [3]:


  
  Leukaemia
  Hypertension
  Coagulation disorders
  Hepatitis
  Head injury
  Myelodysplastic syndromes - Epistaxis
  


Death by massive hemorrhage can occur when epistaxis is the result of a ruptured aneurysm [4, 5, 6]:


  An instance of fatal epistaxis is reported in a patient with an unsuspected aneurysm of the infraclinoid portion of the internal carotid artery. There was no known history of trauma. The aneurysm was subsequently detected on an old X-ray film. Epistaxis from an aneurysm at this site is nearly always preceded by significant head trauma and is associated with cranial nerve palsies, a syndrome with a high mortality. Epistaxis from rupture of a non-traumatic aneurysm is very rare [4].




References:


Work Table I. Deaths from each cause by 5-year age groups, race and sex: US, 1999 Page 1922. U.S. Centers for Disease Control Published 2001-05-11. Via Wikipedia contributors, "Nosebleed," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Nosebleed&amp;oldid=617613780 (accessed July 21, 2014).
QUINN FB. Fatal epistaxis. Calif Med. 1961 Feb;94:88-92. PubMed PMID: 13738727. 
Right Diagnosis (tm). Epistaxis Deaths. Available from http://www.rightdiagnosis.com/symptoms/epistaxis/deaths.htm (accessed 21.07.2014)
HORNIBROOK, J. and RHODE, J. C. (1981), FATAL EPISTAXIS FROM AN ANEURYSM OF THE INTRACRANIAL INTERNAL CAROTID ARTERY. Aust. N.Z. J. Surg., 51: 206–208. doi: 10.1111/j.1445-2197.1981.tb05942.x
P. N. Pathak (1972). Epistaxis - due to ruptured aneurysm of the internal carotid artery. The Journal of Laryngology &amp; Otology, 86, pp 395-397. doi:10.1017/S0022215100075423. 
Urso-Baiarda F, Saravanappa N, Courteney-Harris R. An unusual cause of massive fatal epistaxis. Emerg Med J. 2004 Mar;21(2):266. PubMed PMID: 14988378.