Some XP desktop can no longer connect via Remote Desktop to newer windows releases where the patch MS15-031 (KB 3046049) was installed. I was able to restore connectivity by specifying a GPO setting.
Run gpedit.msc and find “Computer Configuration – Administrative templates – Network – SSL Configuration Settings – SSL Cipher Suite Order”
Enable the setting and paste those values:
TLS_RSA_WITH_AES_128_CBC_SHA256,TLS_RSA_WITH_AES_128_CBC_SHA,TLS_RSA_WITH_AES_256_CBC_SHA256,TLS_RSA_WITH_AES_256_CBC_SHA,TLS_RSA_WITH_RC4_128_SHA,TLS_RSA_WITH_3DES_EDE_CBC_SHA,TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P256,TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256_P384,TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA_P256,TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA_P384,TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA_P256,TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA_P384,TLS_ECDHE_ECDSA_WITH_AES_128_GCM_SHA256_P256,TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA256_P256,TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384_P384,TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA384_P384,TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA_P256,TLS_ECDHE_ECDSA_WITH_AES_128_CBC_SHA_P384,TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA_P256,TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA_P384,TLS_DHE_DSS_WITH_AES_128_CBC_SHA256,TLS_DHE_DSS_WITH_AES_128_CBC_SHA,TLS_DHE_DSS_WITH_AES_256_CBC_SHA256,TLS_DHE_DSS_WITH_AES_256_CBC_SHA,TLS_DHE_DSS_WITH_3DES_EDE_CBC_SHA,TLS_RSA_WITH_RC4_128_MD5,SSL_CK_RC4_128_WITH_MD5
YMMV, try not to enable SSL or TLS ciphers that are to weak for your environment.